Besigye's Forum for Democratic Change (FDC) party said he was detained after checking on reports of an illegal tally centre in his home district manned by the ruling National Resistance Movement party.
"He walked in and saw them pre-ticking ballot papers. They arrested him and took him to an unknown place," said senior FDC official Shawn Mubiru.
There was no immediate police confirmation, but Besigye has been repeatedly detained by police in the past, and is commonly released without charge hours later.
Voting in Uganda's presidential and parliamentary polls failed to begin for several hours in some polling stations in parts of the city and the surrounding Wakiso district, where ballot boxes and papers did not arrive on time.
Also Read
The capital traditionally shows strong support for the opposition.
"A delay of an hour or two is excusable. Delays of three, four, five and even six hours, especially in Kampala, are absolutely inexcusable and will not inspire trust and confidence in the system and the process," Olusegun Obasanjo, the head of the Commonwealth Observer Group in Uganda, told AFP.
After casting his vote in the west of the country the 71-year old incumbent said he was going to have a rest. "I have not been sleeping," he said. "Tomorrow I will go for my cross-country walk to exercise and then go to my cows."
He added that anyone threatening election violence would be "put in the freezer" to cool down.
Ballot counting began even while others still queued to vote in the capital, with polls closing around nightfall.