Wine's National Unity Platform (NUP) said on Friday night that an army helicopter had landed in his compound in Kampala and "forcibly took him away to an unknown destination" - a claim denied by police.
Wine, a former pop star whose real name is Robert Kyagulanyi, said in a post on X that he had managed to flee the raid.
"Last night was very difficult at our home ... The military and the police raided us. They switched off power and cut off some of our CCTV cameras," he said on Saturday.
"I want to confirm I managed to escape from them. Currently, I am not at home."
Wine did not disclose his whereabouts but said his wife and other family members were under house arrest, something Reuters could not immediately verify.
People close to Wine said he was at large in Uganda.
National police spokesperson Kituuma Rusoke had earlier told a media conference that Wine was at home and "not under arrest".
Wine has alleged mass fraud in Thursday's election, held under a widespread internet blackout, and urged supporters to protest.
The vote is widely seen as a test of the 81-year-old Museveni's political strength, and nearly-final results gave him a commanding lead.
As of Saturday morning, Museveni, who has been in power since 1986, had won nearly 72 per cent of votes, with more than nine-tenths of polling stations counted, while Wine trailed on 24 per cent, the electoral commission said.
After a campaign marred by clashes at opposition rallies, and what the United Nations said was widespread repression and intimidation, voting passed off peacefully on Thursday.
But violence broke out in the early hours of Friday in the town of Butambala, about 55km southwest of the capital Kampala, according to police and a member of parliament from the area, who gave differing accounts.
Police spokesperson Lydia Tumushabe said machete-wielding opposition "goons" organised by local MP Muwanga Kivumbi had attacked a police station and vote-tallying centre, and police had opened fire in self-defence.
She said seven people had been killed, three injured and 25 arrested, without elaborating further on the circumstances.
Kivumbi told Reuters 10 people had been killed by security forces about 3am inside his house, where his supporters were waiting for election results for his parliamentary seat to be announced.
"They broke the front door and began shooting inside the garage. It was a massacre," he said.
He said security forces had earlier dispersed crowds outside his house, but disputed the police's assertion that the deaths occurred then.
Tumushabe said she was not aware of any incident at Kivumbi's house, which she said was close to the police station.
Reuters was not able to independently confirm the circumstances of the violence.
