It was not immediately clear who ordered Besigye to be stopped from travelling on the Kenya Airways flight and why the action was taken. No comment was immediately available from the airline or government officials.
Besigye flew to Nairobi two weeks ago after being wounded when Ugandan police dragged him from a vehicle and drenched him in pepper spray to prevent him from taking part in a protest over rising food and fuel prices.
“They have imposed exile on Kizza Besigye. The flight has left without him. Both he and his wife are still in Nairobi,” said Anne Mugisha, deputy foreign secretary of Besigye’s Forum for Democratic Change.
Museveni is due to be sworn in for a fourth term after winning an election in February in which Besigye was his closest opponent.
Reuters witnesses in Kampala said there was a heavy security presence on the streets.
On Tuesday, Museveni said he would change the law to deny bail to people accused of rioting and economic sabotage, in a further crackdown on opposition protests.
Museveni, in power for 25 years, accused the opposition of trying to spread chaos to avenge its loss in the election, which he won with 68 percent of the vote.