This is largely the result of Stalin's deportations.

Starting in the late 18th century the Russian Empire (in the form of its German-born Empress Catherine the Great) invited thousands of German farmers to settle the newly conquered lands in the south, along the Volga River and in Ukraine (I'll disclose my own family background is German farmers from Ukraine). This was to help develop the land, which at the time was sparsely populated, and import some European cultural norms to the Russian peasantry. Thousands of Germans settled the region, keeping their language and customs. By the Soviet era they numbered in the hundreds of thousands, and a separate autonomous republic (the Volga German Autonomous Republic) was established within the USSR to serve their interests.

Then the Second World War started, specifically the German invasion of the Soviet Union. While the ethnic Germans had been seen with some suspicion in the 1930s, and there were some efforts to repress them within Ukraine and the borderlands, it was in August 1941 that the real measures began. The entire community was expelled from their homeland, as the authorities feared they would aid the rapidly-advancing German military (never mind that the Volga Germans hadn't been in Germany in centuries, to the point that they didn't even speak the same dialects of German anymore). More than 400,000 people were sent to Central Asia; most went to Kazakhstan but a significant number also ended up in Kyrgyzstan (they peaked at about 3% of the Kyrgyz population, in 1970), while thousands died en route or shortly after reaching there.

This was of course not an isolated event, nor were the Germans the first ethnic group deported to Central Asia. In 1937 the ethnic Koreans in the Far East were shipped to the region, mainly Uzbekistan, as the Soviets feared they would ally with the Japanese (who had occupied Korea since 1910). Then of course in there were various deportations throughout the rest of the Second World War: the Chechens, Kalmyks, Crimean Tatars, Mesketian Turks, Karachays, among others. Hundreds of thousands of people were accused of being collaborators with the Nazis and shipped en mass to Central Asia.

These groups, along with the Germans, were forbidden to leave their settlements, and while some regulations were relaxed after the death of Stalin in 1953, it was not until the 1970s that the Germans were given free reign again. Having spent three decades in Kazakhstan at this point, many had nowhere else to go, and simply remained there. The reunification of Germany in 1989 saw this change slightly as the German government invited many of these people to come settle in Germany, which combined with the turmoil of the collapse of the Soviet Union in 1991 saw a massive decrease in population there. However ethnic Germans still make up 1% of the population of Kazakhstan today (down from 7% in 1959).