The man identified by police as Charlie Grieves-Cook was pronounced dead on arrival in hospital.
A guard who attempted to confront the armed thugs was shot and seriously wounded, but police said Sunday he had been declared out of danger.
Apart from being the proprietor of a tour firm, Grieves-Cook is also a renowned photographer in the region.
“He fell badly after jumping from the balcony and he died on arrival in hospital,” Nairobi PPO Antony Kibuchi said and assured that an investigation into the incident has been launched.
Area divisional Police chief David Bunei said no arrests had been made by Sunday afternoon.
“We will definitely get them (attackers). Immediately the man fell down, there was confusion all over, the thugs did not manage to enter the house,” Bunei said. “They fled immediately and that is when they opened fire at the guard and wounded him.”
Bunei said the man was in the company of woman walking upstairs when the confrontation occurred.
“We are told the two men were just walking casually upstairs following the deceased and the lady, that is when they confronted them and it appears they wanted to force them into the house, sparking a confrontation,” Bunei explained.
The incident occurred at an apartment on Lang’ata road near Uchumi Supermaket.
By the time police arrived at the scene, the man had been rushed to hospital where he was pronounced dead on arrival. His body was taken to the Lee Funeral Home.
In another incident, two Kenya Wildlife Service (KWS) rangers were gunned down at the weekend and their firearms taken away during an attack near Tsavo East.
The two, including a female officer were on patrol near Sagala ranch when armed bandits confronted them.
KWS Spokesman Paul Mbugua said they believe the bandits escaped with gun shot injuries and have launched a man hunt for them.
“These officers were ambushed, and there was a shoot out before they were shot dead. A massive security operation was mounted immediately and we hope to find them,” Mbugua said.
He said the officers were removing snares from the park when the attack occurred.
KWS has sent out an appeal to residents in the region and hospitals to notify police of people seeking treatment with gun shot wounds.
“We have every reason to believe they escaped with injuries, because there was a shoot out during the attack, we are urging residents to work closely with us,” Mbugua said.