He did.

Towards the end of his life several raids were made on the Punjab region. Subsequent Mongol rulers invaded and occupied Kashmir. Further inroads were difficult due to the massive Delhi Empire which inflicted many defeats upon the Mongols, and repeated rebellions in occupied regions. The geography of the region also required going around the Himalaya mountains and through the deserts around Afghanistan.

Later descendants of Mongols had much greater success. Timur, a descendant of Mongols (though not of Genghis' loins himself) and his heirs conquered much of India in the name of the Timurid, and Mughal Empire, as it was later known.

I have attempted to answer this question in a previous comment However I do not feel like I have done it justice. Here is the Tl;dr

Essentially, Ghenghis Khan and following Mongols did invade India a few times but due to geography, weather and fortification of the subcontinent, the Mongols were kept at bay. I have come across references to the extreme heat of India being a primary issue as compared to the cool Mongolian-held steppes. The Mongols under Ghenghis Khan would not conquer India, but the Mughal Dynasty descended from the Mongols established by Babur would come to conquer the subcontinent.

Sources:

Avari, Burjor. India: The Ancient Past (2007) Smith, Vincent. The Oxford History of India (1958 and its later editions touch on this)