An eyewitness told Belarus news outlet Tut.by that she saw masked men take Ms Kolesnikova’s mobile phone and push her into a minibus on Monday morning.
Police in the capital, Minsk, have not yet commented on the reports.
Ms Kolesnikova was a member of the Co-ordination Council set up by the opposition to ensure a transfer of power.
Government authorities have launched a criminal case against opposition leaders, saying the “creation and activity of the Co-ordination Council are aimed at the seizure of state power, and at harming national security”.
She is the last of the three women who joined forces against Mr Lukashenko to remain inside Belarus. Veronika Tsepkalo and presidential candidate Svetlana Tikhanovskaya left the country soon after the vote.
Ms Tikhanovskaya said the latest detentions were an attempt to disrupt the work of the Co-ordination Council.
“The more they try to scare us, the more people will take to the streets,” she said in a statement.
Meanwhile, the Co-ordination Council said Ms Kolesnikova’s whereabouts were “unknown” and accused President Lukashenko of “openly using methods of terror”.
In an interview with BBC Russian last month, Ms Kolesnikova described the recent anti-government demonstrations as “not a struggle for power” but “a struggle for human dignity and self-respect”. She said she and her team had decided against using bodyguards because there would be “no point”.
“I am aware that no number of guards would be of any use if a bus full of riot police stopped us,” she said. “We all know what a police state is capable of.”
Another female activist, Olga Kovalkova, announced on Saturday that she had fled to Poland amid threats of imprisonment.
What happened on Sunday?
Her arrest follows further demonstrations on Sunday – a key day for street demonstrations since the rallies began.
Eyewitnesses told Russia’s Interfax news agency that police began to make arrests in Minsk after the unsanctioned rally ended and people were going home.
Video footage on Sunday shows men in plain clothes beating peaceful protesters with batons.
The interior ministry confirmed at least 633 arrests had been made across the republic. It said some 363 people had been sent to detention centres pending court hearings.
Internal Affairs Minister Yuri Karayev defended the actions of the security forces.
“They talk about the brutality of the Belarusian police, and I want to say this: there are no more humane, restrained and cool-headed police anywhere in the world,” he was quoted as saying by the official Belta news agency.
In recent days, the security forces have targeted university students as they returned from their holidays, dragging some from the streets and university buildings into unmarked minivans.
One protester in Minsk, who gave her name as Lyudmila, told the BBC earlier that the demonstrators were undeterred by the security forces.
“We are definitely not ready to get back to the life we had for many years now,” she said.
“We finally feel like we matter because we’ve been living in apathy for way too long, and now we just have this feeling of solidarity and we actually think that – well, I feel personally that – changes already are happening, so that’s definitely not the time to give up.”
Protests have also been reported in other Belarusian cities and towns including Grodno, Mogilev and Gomel.