Protesters are calling for the election results, which overwhelmingly declared incumbent President Alexander Lukashenko the winner, to be annulled.
"Alexander Dobrovolsky, Anatoly Lebedko, Alexei Yanukiyevich and Valentina Pavelikova were arrested as they were leaving the square," said Pavel Mazheika, a spokesman for Mr Milinkevich.
He added that several other people protesting at the re-election of President Lukashenko had been detained overnight.
Mr Lebedko is head of the United Civil Party (UCP), a liberal group that selected Mr Milinkevich, a 58-year-old former physics professor, to represent the United Democratic Forces coalition that challenged Mr Lukashenko in Sunday's presidential electon.
Pavelikova and Dobrovolsky are heads of the UCP's Minsk branch, Russia's Interfax news agency said.
Sanction threat
Earlier, the US rejected the result of the election, and along with the EU, threatened the Lukashenko government with new sanctions.
"The United States does not accept the results of the election," White
House spokesman Scott McClellan told reporters.
"We applaud democrats in Belarus for their courage and peaceful stand to reclaim their freedom," he added.
"We support their call for a new election."
Mr McClellan said the US, in cooperation with European partners, would consider new sanctions on the hardline regime of Mr Lukashenko, who, according to official results, won 82.6 percent of the vote in Sunday's controversial poll.
"Certainly travel restrictions and targeted financial sanctions of individuals are things that we will look at," the White House spokesman said.
The US State Department reaffirmed the rejection of the election.
"The United States is preparing to take serious appropriate measures against those officials responsible for election fraud and other human rights abuses and will be coordinating these steps with the European Union," said State Department spokesman Sean McCormack.
The European Union has said it will almost certainly increase its existing sanctions against the Belarus government.
The Organisation for Security and Cooperation in Europe (OSCE), which sent 400 monitors to the former Soviet republic, earlier condemned the conduct of Sunday's ballot, as did the European Union and NATO.
"The March 19 presidential election does not meet the required international standards for free and fair elections," said Alcee Hastings, who coordinated the more than 400 OSCE observers during the election.
"It is clear that the incumbent president allowed the state authorities to be used in a manner which did not allow free and fair elections," he said.
Protests continue
Opposition supporters remain camped on the main square of the capital Minsk, after spending the night demonstrating.
More than 300 people remained, in defiance of a government ban and despite freezing conditions.
Activists erected tents and sang and danced to keep warm.
Mr Milinkevich remained at the protest until dawn, calling on supporters to return in the evening.
"It's a victory of the people over fear," he told AFP.
"I didn't think this would be possible," he said.
While police mostly kept a discreet presence, Mr Lukashenko and his security chiefs have vowed a harsh response to what they say are opposition plans to seize power by force.