In the capital Minsk, live feeds from Radio Free Europe showed riot police using tears and stun grenades to disperse protesters.
Tikhanovskaya, 37, said at a news conference late Sunday that she did not agree with the results. Her campaign claimed that at that time she had won in dozens of polling stations in Minsk.
Monitoring organization Golos said it counted more than a million ballots and according to its calculations, Tikhanovskaya won 80% of the vote.
Final results will be announced on Monday.
Tikhanovskaya, a former English tutor, became an unexpected rival and the face of the opposition after taking over from her husband, Sergey Tikhanovskiy, a popular YouTube blogger and former candidate who has been imprisoned since May.
Their campaign rallies saw important missions even in small Belarusian cities not known for their protest activity. Some 63,000 people attended the largest event in Minsk in July – making it the largest demonstration in decades.
Tikhanovskaya went along with two women who ran other opposition campaigns, after their candidates were also prevented from running or imprisoned. Lukashenko on Tuesday dismissed her as “poor girl” in his annual statement from the union, saying he would not “give away the land.”
Tikhanovskaya’s campaign manager Maria Kolesnikova was also taken to a police station for questioning on the eve of the vote. A day earlier, campaign manager Maria Moroz had been briefly arrested.
Nicknamed “the last dictator of Europe”, Lukashenko has ruled the former Soviet republic of more than 9 million people since 1994. He has long drawn international criticism for suppressing dissent, and the country’s secret police – still known as the KGB – often arrests and harass activists and independent journalists.
The poll saw a massive turnout, according to official data, with the country’s Central Election Commission reporting 65.19% turnout from 2am local time Sunday.
However, internet access is largely limited, and was completely shut down in central Minsk, according to local reports.
NetBlocks, an NGO that monitors international shutdowns worldwide, said in a tweet late on Sunday, “Several internet providers in #Belarus have lost routing as polling stations start at 8pm; geolocated network data confirm the new disrupting nation scale has affected visibility of events further restricted. “
Most apps and websites took longer to load, including Whatsapp, Viber and Facebook Messenger. Telegram Messenger, which serves as the main means of communication for the Belarusian opposition, was sometimes unavailable or only accessible via proxy servers.
Independent observers in Belarus, such as the “Real People” Volunteer Monitoring Group, said they also found significant discrepancies between the officially announced turnout and the number of people in polling stations they could count.
Most independent observers were prevented from overseeing the elections. Thousands of independent observers were arrested on Saturday and early Sunday, according to the “Honest People” and “Right to Choose” initiatives.
The Organization for Security and Cooperation in Europe said in July that it would not send observers to Belarus because it had not been invited by the country’s authorities.
The foreign ministries of France, Germany and Poland said they would monitor the elections with “great concern” because of “concern reports of irregularities in the elections during voting.” The three countries said the European Council was also not allowed to monitor the election process.
Journalists Mikalai Anishchanka in Minsk and Barbara Wojazer from CNN contributed.
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