Kizza Besigye was detained during a raid on his party’s headquarters in the capital, Kampala, following Thursday’s tightly contested elections.
Police also fired tear gas to disperse his supporters.
The US urged President Yoweri Museveni, who is seeking to extend his 30-year-rule, to “rein in his police”.
With official results for nearly half of the polling stations declared, Mr Museveni is leading with 62% of the vote, while Mr Besigye has 33%.
Mr Besigye’s supporters say the result is being rigged to rob him of victory.
This is the third time in the space of a week that the opposition candidate has been detained.
He was released on the two previous occasions without being charged.
There is a heavy deployment of soldiers and police in parts of Kampala, says the BBC’s Catherine Byaruhanga in the city.
There have also been reports of some clashes between the security forces and opposition supporters, she adds.
Mr Besigye was arrested because he planned to announce “purportedly final results” in breach of electoral laws, police said in a statement.
His action would have amounted to “disturbing public order”, police said.
US Secretary of State John Kerry telephoned Mr Museveni, and told him that the arrest “calls into question Uganda’s commitment to a transparent and credible election process free from intimidation”, the state department said in a statement.
The US embassy in Uganda condemned the crackdown in a post on its Twitter account.
The US also criticised the shutdown of social media, chat apps and mobile money services in Uganda on Thursday.
President Museveni said the decision had been taken for security reasons, and to prevent people from “telling lies”.
Voting was extended to a second day at a few polling stations, where election material arrived up to five hours late on Thursday.
The Commonwealth election observer mission head, Nigeria’s former President Olusegun Obasanjo, said the lengthy delay in opening polling stations was “absolutely inexcusable and will not inspire trust and confidence in the system and the process”.
Ugandans also voted in parliamentary and local elections.
Final results are expected on Saturday.
Major presidential contenders:
- Kizza Besigye, 59, veteran opposition leader and once personal doctor to incumbent President Museveni. He has lost the last three elections
- Amama Mbabazi, 67, former ally of President Museveni and once prime minister and also served as defence, security and justice ministers
- Yoweri Museveni, 71, in power since winning a five-year guerrilla war in 1986 and he is one of Africa’s longest-serving leaders. His final term was meant to end in 2006, but in 2005 he won a campaign to lift the constitutional term limits.