The 38-year-old is Mr Museveni’s main rival and is particularly popular with the country’s youth, leading the regime to target him and his supporters during his presidential campaign.
He has been arrested numerous times in recent months and has allegedly survived several assassination attempts.
In a tweet posted on Friday afternoon, Mr Wine said: “We are under siege. The military has jumped over the fence and has now taken control of our home.”
“We are in serious trouble,” he added in another message.
The singer turned politician has claimed that Thursday’s election was rigged, adding that “every legal option is on the table” and referring to himself as “president-elect”.
Although the final results will not be released until Saturday afternoon, Uganda’s electoral commission said Mr Museveni, who has ruled the country for 35 years, was leading Mr Wine by 62 per cent to 29 per cent, with roughly half of all votes counted.
Mr Wine told reporters on Friday that “whatever is being declared is a total sham”. “I am very confident that we defeated the dictator by far,” he added.
The violence in the run-up to the election has been widely condemned, with the UN saying earlier this month that it was “deeply concerned by the deteriorating human rights situation in Uganda”.
This view was shared by Josep Borrell, the EU’s high representative, who said: “The excessive use of force by law enforcement and security agencies has seriously tarnished this electoral process.”
Between 18 and 20 November, more than 50 people were killed when security forces tried to break up opposition rallies.
The incumbent president, whose support base is strongest in rural communities, has done little to hide his strong-arm tactics. In a televised speech on Tuesday, Mr Museveni told his supporters: “There is no threat we cannot defeat. We have got all sorts of means, simple and complex.”
Neither the EU nor the US sent officials to observe yesterday’s election, after the bloc’s previous advice was ignored and US officials were denied visas for the trip.
However, those on the ground have noted problems with the election. One member of a leading Ugandan election observer group was reportedly arrested while meeting a journalist in Kampala.
Ahead of the election, Mr Museveni told internet providers to block all social media use in the country, before the government fully cut the internet on the eve of the vote.
On Thursday, Mr Wine said that the government had blocked his phone to stop him communicating with his election team.