Bobi Wine was arrested during an election rally in the eastern district of Luuka after being accused of violating coronavirus guidelines set by the electoral commission.
His supporters have called for his release.
Police said three people died and dozens were injured in the protests.
The US mission there has urged “all parties to renounce violence” and to undertake measures to reduce tensions.
The United States deplores the violence that has claimed multiple lives today, and we extend our sympathy to the victims’ families and loved ones. We urge all parties to renounce violence, undertake good-faith measures to reduce tensions, and respect fundamental freedoms. pic.twitter.com/FewY3RgMNw
— U.S. Mission Uganda (@usmissionuganda) November 18, 2020
Uganda will hold presidential elections in January.