"During the rally, Kozulin urged power overthrown, state facilities attacked and the head of state killed," Vladimir Naumov said at a briefing.
The minister said one civilian and eight servicemen and policemen had been injured during the unsanctioned rally. Naumov said the police had done its best to prevent military force from being used to disperse the rally.
In Sunday's polls, Kozulin and two other candidates challenged President Alexander Lukashenko, dubbed "Europe's last dictator" by Washington. According to official results, the incumbent won a landslide victory with 83% of the vote; main opposition candidate Alexander Milinkevich garnered 6.1%; Liberal Democrats Chairman Sergei Gaidukevich, widely regarded as a Lukashenko loyalist, finished third with 3.5%, and was followed by Kozulin with 2.3%.
The opposition disputed the official election returns on Monday, taking to the streets to call for a re-run.
Milinkevich blamed the consequences of the rally, originally planned as peaceful, on Kozulin, adding that the latter had made "more than a mistake" when he urged people to go to a detention center where reportedly several hundred people who had taken part in unsanctioned rallies were kept.