Is there a height limit?

There is a height limit in GTA 5 as well, yes.

Previously, the one in GTA 5 is 12800 ft, which is around 4000m respectively.
Old wiki page

This wiki page has been updated on December 2014 to change these limits. It's now indicate that the limit is 8100 ft (2470m), which coincide with Bens' answer.
Actual wiki page

Cheers.