However Russia’s President Vladimir Putin is backing Mr Lukashenko.
The opposition says Mr Lukashenko must quit. But he says they are Western “puppets” trying to overthrow him.
Ms Tikhanovskaya has been visiting Berlin to discuss the crisis with Chancellor Angela Merkel and other German officials.
EU sanctions now target 40 Belarus officials, but not Mr Lukashenko himself.
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What is the charge against Ms Tikhanovskaya?
Russia’s interior ministry did not give details of the charge against Ms Tikhanovskaya.
But Russia’s Tass news agency reported that she was on the wanted list in Belarus and the Belarusian warrant against her would also be carried out in Russia according to agreements between the two countries.
However she was not on an international wanted list, a source told Tass.
Ms Tikhanovskaya was forced to go into exile in Lithuania after receiving threats following the disputed vote.
She only stepped in to challenge Mr Lukashenko for the presidency after her husband, a popular blogger, was barred from running and sent to jail.
Ms Tikhanovskaya has repeatedly appealed to the international community to put pressure on Mr Lukashenko so that a democratic transition can be launched by negotiation.
Earlier on Wednesday Kremlin spokesman Dmitry Peskov said Mr Putin had no plans to meet Ms Tikhanovskaya.
“No contacts are being planned,” he said. “Madame Tikhanovskaya is not in Belarus. One can hardly say that she is somehow involved in Belarus’s life.
“She is meeting with various heads of state and government who consider Belarus’s sitting president illegitimate,” he added.
What is happening in Belarus?
Weeks of anti-government demonstrations since the disputed election have seen tens of thousands of protesters on the streets in cities across the country.
Many opposition activists have been beaten up by police and thousands have been arrested during months of unrest. They are demanding the release of all political prisoners and a free and fair re-run of the election.
Many of Ms Tikhanovskaya’s supporters and allies have been detained, on the charge of making public calls to harm the country’s security, or forced to leave the country after receiving threats from the authorities.
Meanwhile four more EU nations, including Germany, are recalling their ambassadors to Belarus in solidarity with Lithuania and Poland, the Lithuanian foreign ministry said on Wednesday.
Belarus says Lithuania and Poland are interfering in its internal affairs by hosting Ms Tikhanovskaya and other opposition figures and refusing to accept the election result.
Belarus recalled its ambassadors to Poland and Lithuania last Friday and told both countries to reduce the number of staff at their embassies in Minsk. They refused and recalled their own ambassadors.