Speaking to Reuters via Skype, Linas Antanas Linkevicius also said EU sanctions are possible against Belarus officials who used force against peaceful protesters.
"Crackdown in Belarus after the election is unacceptable and we cannot tolerate it and there should be some political consequences," Linkevicius added.
Tikhanouskaya, who has Lithuanian visa and can stay in a Baltic stay for up to a year, said on Tuesday she had fled abroad for the sake of her children, after two nights of clashes following the contested re-election of strongman President Alexander Lukashenko.
Both she and the Belarusian authorities said she had not been forced to leave.
There had been concern about Tikhanouskaya's whereabouts after her campaign team said on Monday they had been unable to reach her by phone hours after she was known to have left a meeting with central election commission officials.
At least one person died as police clashed with protesters on Monday (August 10) after the opposition accused Lukashenko of rigging the vote amid widespread criticism from Western leaders.