Belhassen Trabelsi, a billionaire Tunisian businessman and brother of former first lady Leila Trabelsi, reportedly arrived in Canada last week with his family.
As the first lady's oldest brother, he was known as the Trabelsi clan chieftain and is suspected of running the family's many mafia-style rackets.
Foreign Affairs Minister Lawrence Cannon told The Canadian Broadcasting Corp. that Trabelsi has submitted a claim for asylum.
Cannon had said earlier that the government would try to comply withTunisia's extradition request, but under Canadian law, it could take years to decide the asylum and extradition cases, given the lengthy appeals process.
"We've indicated that these people are not welcome in Canada, but obviously that having been stated, Canada is nonetheless a country that has legislation," Cannon said. "We do abide by the rule of law."
Canada also said it will also freeze Trabelsi's assets. Cannon said every effort will be made to track down his accounts.
Trabelsi fled to Montreal with his family after an uprising toppled Ben Ali. It was not clear where Trabelsi went first after fleeing Tunisia. France had said some Ben Ali relatives went there, but were "not welcome" to stay.
Trabelsi has permanent resident status in Canada, although officials suggested his residency status could be revoked because he has not spent at least two of the last five years here, as required by law.
Cannon said authorities are in contact with Trabelsi's lawyer in Montreal.
Huge street protests forced Ben Ali to flee to Saudi Arabia on Jan. 14 after 23 years in power. Tunisia has issued an arrest warrant for the ousted leader, accusing him of taking money out of the country illegally and other charges. Interpol said its Tunis bureau issued a global alert seeking the arrest of six family members, but their names have not been made public.
Ben Ali, his wife and their clan have been widely accused of abusing their power to enrich themselves. In France, where family members are believed to have assets ranging from apartments to racehorses, Paris prosecutors have opened a preliminary investigation into their holdings.
Nejmeddine Lakhal, a spokesman at Tunisia's embassy in Ottawa, said the embassy had received the extradition request for Belhassen Trabelsi and forwarded it to Canada's foreign affairs department. He said Trabelsi's diplomatic passport has been canceled.
Leila Trabelsi, a one-time hairdresser, rose to become Tunisia's most influential woman. Leila and her 10 siblings are said to have operated like a mafia, extorting money from shop owners, demanding a stake in businesses large and small, and divvying up plum concessions among themselves.
The Trabelsi and Ben Ali families were said to have a stake in Tunisian banks and airlines, car dealerships, Internet providers, radio and television stations, industry and big retailers.
A new transition cabinet was sworn in on Saturday in Tunisia and interim Prime Minister Mohammed Ghannouchivowed a transition to democracy and an economic revival.
"We urge the new unity government to prepare for free and fair elections as a way of addressing the legitimate democratic aspirations of the Tunisian people," Cannon said Saturday. "In the interim, we urge the government to continue its consultations with all Tunisians as it builds a new society committed to democracy, human rights and the rule of law."