In the capital, Minsk, live feeds from Radio Free Europe showed riot police using tear gas and stun grenades to disperse protesters.
Tikhanovskaya, 37, said in a news conference late Sunday that she did not agree with the results. Her campaign maintained that she had won in dozens of polling stations in Minsk at that stage.
Monitoring organization Golos said it counted more than a million ballots and, according to its calculations, Tikhanovskaya won 80% of the vote.
Final results are due to be announced 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 jailed since May.
Her campaign rallies saw significant turnouts even in small Belarusian towns not known for their protest activity. About 63,000 people attended the largest event in Minsk in July — making it the biggest demonstration in the past decade.
Tikhanovskaya joined forces with two women who ran other opposition campaigns after their candidates were also either barred from running or jailed. Lukashenko had dismissed them as “poor girls” in his annual state of the union address on Tuesday and said he will not “give the country away.”
Tikhanovskaya’s campaign manager Maria Kolesnikova was also taken to a police station for questioning on the eve of the vote. A day before that, campaign manager Maria Moroz was briefly detained.
Nicknamed “Europe’s last dictator,” 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 detain and harass opposition activists and independent journalists.
The poll saw a massive turnout, according to official data, with the country’s Central Elections Committee reporting 65.19% turnout as of 2 p.m. local time Sunday.
Yet internet access has been largely restricted, and was completely shut down in central Minsk, according to local reports.
NetBlocks, an NGO that tracks internet shutdowns worldwide, said in a tweet late Sunday, “Multiple internet providers in #Belarus have lost routing as polling stations start to close from 8:00 p.m; geolocated network data confirm the new disruption has nation-scale impact further limiting visibility of events.”
Most apps and websites were taking longer to load, including Whatsapp, Viber, and Facebook Messenger. Telegram Messenger, which serves as the main communication tool for the Belarusian opposition, was unavailable at times or only accessible via proxy servers.
Independent observers in Belarus, such as the “Honest people” volunteer monitoring group, said they also found significant discrepancies between the officially announced turnout and the number of people entering polling stations that they were able to count.
Most independent observers were barred from monitoring the election. Dozens of independent observers were detained 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 it would not be sending observers to Belarus as it hadn’t been invited by the country’s authorities.
The foreign ministries of France, Germany and Poland said they would be monitoring the elections with “great concern” due to “worrying reports of electoral irregularities during early voting.” The three countries said the European Council was also not allowed to oversee the electoral process.
Journalist Mikalai Anishchanka in Minsk and CNN’s Barbara Wojazer contributed.