This is somewhat true, but misses the main reason why the voyages were discontinued. The voyages were discontinued because of their cost, as well as internal political conflicts between the traditional Confucian bureaucracy and the eunuchs.

The leadership of the Ming Dynasty believed (correctly) that they were possessed of the most advanced and powerful empire in the world. For this reason, they were not particularly interested in overseas trade in the same way that the Europeans were. To the extent that other cultures had things the Chinese wanted, the Middle Kingdom could get them in the form of the tribute system.

These were also not voyages of "exploration" like the European ventures. The Chinese didn't go anywhere that they weren't already familiar with. They had very detailed maps that included the coasts of Asia and East Africa.

So why did they launch the voyages in the first place? Probably because the Yongle emperor wanted to do something his father hadn't, to stake his own claim to glory. The ostensible reason given at the time was to search for an escaped prince. And maybe, perhaps, they could establish new tribute relations with people in more far-flung areas.

However, the farther away the voyages went, the Chinese seemed to encounter societies that were more poor and less advanced than their own. Aside from curiosities such as large animals from Africa (like giraffes and rhinos), the voyages did not seem to be yielding much of value.

Furthermore, at the same time as the voyages, the previously divided and feuding Mongol tribes were beginning to unite and launch military offensives against the Ming. This was especially scary for the Ming Dynasty since the Yongle emperor had relocated the capital to Beijing, putting the leadership much closer to a resurgent Mongol confederation.

In addition, the Confucian bureaucracy chaffed under the growing influence of eunuchs (the leader of the navy was a eunuch admiral named Zheng He), and when the Yongle emperor died, they were eager to reduce the power of the eunuchs in the government. The voyages were, in the minds of the Confucian bureaucrats, a costly form of adventurism that was conceived by un-scholarly eunuchs who didn't know what proper governmental priorities should be -- namely safety and security from the Mongols, and improving China's internal economy.

A good analogy would be with the United States and space exploration. At the height of the Cold War the United States spent a pretty substantial portion of the federal budget on NASA. Today we only spend a fraction of this. It isn't because people are opposed to the idea of space exploration in general, it is just a question of political priorities.

Now this probably isn't the question you're asking, and I see others have answered regarding the cessation of the Ming treasure voyages, so I'll chime in about the "dismantlement" of the Chinese navy.

For much of its history, China did not have anything like a national navy, and its first standing navy was established during the Song dynasty in the 12th century. Even so, the focus of this navy was riverine in nature, since the Song dynasty was mostly concerned with defending its river borders against the Jurchen Jin dynasty, and later the Mongol Yuans. For the eastern coast, the threat of an attack was considerably less, and thus the was less of an emphasis on a coastal navy. In a telling episode, when the Mongols overran the Southern Song capital of Lin'an the Southern Song court had to bargain with the Muslim merchant Pu Shougeng for ships to flee south, showing just how lacking the Song coastal was. Instead, Pu Shougeng threw in his lot with the Mongols, and in 1279 his ships were part of the fleet that demolished the last remaining resistance at the Battle of Yaishan.

Under Mongol rule, maritime trade continued like it had during the Song dynasty, but as the Mongol Yuan gave way to rebel regimes, trade became disrupted. The Ming dynasty came to power after besting other rebel regimes in a series of battles, with one of the most celebrated one being the naval Battle of Poyang Lake. One of the immediate concerns of the new Ming Hongwu emperor was the elimination of his remaining enemies. Some of them had ties with Japanese pirates, and so in 1371 he banned private overseas trade in order to clear the seas of piratical elements and to funnel all overseas trade to the imperial treasuries. To further defend the coasts from Japanese pirates, he introduced the weisuo system (衛所) on the offshore islands, in what Stephen Turnbull calls the "Great Wall of the Sea". What it is is that garrisons are stationed along the shoreline to the on the watchout for pirates, and when sighted, the coast guard is sent out to meet them before they can come ashore. The weisuo system on the sea and the treasure voyages gave the early Ming dynasty much naval prestige, and with it the Ming projected their power from Japan all the way to the coast of Africa.

A note here on the treasure voyage: adding to the reasons that /u/FabianJanowski already listed, there is an economic reason as well. The treasure voyages were a form of tributary trade, in which foreign countries present tribute to China to give its emperor prestige and legitimacy, which China gives back gifts for their trouble. The way this trade works in China's favour is when China is able to make the foreigners accept its paper money, and while China's navy can intimidate its neighbours and inspire confidence in China's economy, the foreigners were glad to take them. Otherwise, the foreigners would demand actual goods like silk and porcelain. So when the Ming navy lost its prestige, it was no longer profitable for the government to send ships out to faraway places to enforce tributary trade.

Over time, the Mongol threat had drawn the attention of the court in Beijing, especially after the Ming emperor had been captured by the Mongols in a military debacle in 1449. After that, Ming policy turned from expansionist to defensive, and the court was forced to withdraw many outlying garrisons in order to save money. It is important to note that by this time, the Ming capital had moved from Nanjing, which faces the sea, to Beijing, which faces the steppes. The coast had long been peaceful since the early Ming dynasty, and so the coastal population did not see a reason to continue maintaining the defenses on the islands. So the coast guard was abolished and many warships were allowed to fall into disrepair. The new rationale was that if pirates do appear, instead of intercepting them at sea, the coastal garrison could beat them on the shoreline. With the government retreating from the sea, the coastal gentry resumed sponsoring seafarers to trade overseas, flouting the Ming sea ban. This would lead up to the great wokou raids of the 16th century, in which "Japanese pirates" (actually Chinese pirates sponsored by the Chinese gentry) were blamed for the destruction the raids wrought on the Chinese coast. The Chinese maintained interest in the world beyond their borders, but it was not by the government - they gave it away to private traders when they themselves could not afford to maintain their fleets.