The two have not yet been named.
Witnesses say the chopper was taking off when it came down a few seconds later and exploded into flames.
“I just saw the chopper drop and burst into a ball of flames before the rescue operation started,” said a private security guard at the busy airport.
Police said one of the Zambians is the owner of the ill-fated aircraft.
“Preliminary findings show the chopper developed mechanical problems immediately after taking off,” said Airport CID boss Joseph Ngisa.
The chopper is said to have come from Juba, South Sudan and had made a stop-over at the busy airport.
“I understand they were headed for Tanzania,” he said.