Mr Lukashenko, who has led Belarus since 1994, insists he has won fairly and has ruled out holding another election.
What happened on Tuesday?
Hundreds of opposition supporters gathered outside the jail in the capital, Minsk, where Mr Tikhanovsky is being detained on charges of inciting violence.
Many held red-and-white balloons - the colours of the opposition - and sang "happy birthday".
Ms Tikhanovskaya, 37, said her husband was spending his birthday in prison because of "a crime he did not commit".
"All of this blatant lawlessness and injustice shows how this rotting system works, in which one person controls everything, one person who has kept the country in fear for 26 years, one person who robbed Belarusians of their choice," she said in a video message.
Ms Tikhanovskaya says that where ballots were properly counted, her share of the vote ranged from 60% to 70%.
In another video message released on Monday, she said she was ready to become a "national leader" to restore peace and prepare for new elections.
How strong is the pressure on Lukashenko?
On Sunday, more than 100,000 people gathered in Minsk for the largest protest held in Belarus since it declared independence from the Soviet Union in 1990.
Strike action is also keeping up the pressure on the president. State TV and key factories have been affected and on Tuesday postal workers reportedly joined the strikes.
A number of officials, as well as current and former police officers, have resigned.