The incident occurred at 1005 local time (0705 GMT) between a plane belonging to a flying school and a Safarilink passenger aircraft, Kenya's Civil Aviation Authority said in a statement.
Local airline Safarilink said passengers on its plane bound for the coastal resort of Diani were unharmed.
"I can confirm a student and a trainer (on the training aircraft) ... died during the incident," Nairobi County police commander Adamson Bungei told Reuters without providing more details.