Overnight, Wine’s party said that he had been abducted from his home in the capital, Kampala – a claim denied by the police.
Wine later issued a statement on Facebook saying that he had managed to evade a night-time raid by security forces and was in hiding.
He had previously said he was under house arrest.
This has not been confirmed by the police but spokesman Kituuma Rusoke said Wine’s movements had been restricted because his home was an area of “security interest”.
“We have controlled access to areas which are security hotspots,” Uganda’s Daily Monitor paper quoted him as saying.
“We cannot allow people to use some places to gather and cause chaos,” he said.
Wine says he represents the youth in a country where most of the population is aged under 30.
During the campaign, he promised to tackle corruption and impose sweeping reforms, while Museveni argued that he was the sole guarantor of stability in Uganda, a country with a history of conflict.
There were six other candidates but none got more than 2% of the vote. Turnout was 52.5%.
The campaign period was marred by the disruption of opposition activities – security forces have been accused of assaulting and detaining Wine’s supporters.
Rusoke, the police spokesperson, dismissed these complaints, accusing opposition supporters of being disruptive.