The decision was taken after the Government of Kenya announced this morning that it was postponing all meetings and conferences in the country of an "international nature".
Keith Pelley, the European Tour's chief executive, said: “We understand and totally respect the decision made by the Government of Kenya in these difficult times.
“We are looking into the possibility of rescheduling the tournament at some point later in the season, but that remains simply a possibility right now – we have no definitive plans at this stage."
The event, which was due to be held at Karen Country Club in Nairobi, joins the Maybank Championship and Volvo China Open on the circuit's casualty list due to the spread of COVID-19.
It leaves the Hero Indian Open in a fortnight's time as the only regular event on the schedule after this week's Qatar Masters until the Andalucia Masters at the end of April.
Three upcoming events in Egypt were also postponed today on the Alps Tour, one of the third-tier circuits.
The Allegria Open, the Dreamland Pyramids Open and the New Giza Open are all being rescheduled for September.
The MENA Tour, another third-tier circuit based in the Middle East and North Africa, announced yesterday that it was cancelling six upcoming events on its schedule.
Other events to have been cancelled in recent weeks include the HSBC Women's Champions in Shanghai and the Women's Amateur Asia-Pacific Championship.
On Tuesday, Augusta National chairman Fred Ridley said it was all systems go at the moment for next month's Masters, the opening men's major of the season, though the ongoing situation is being closely monitored.