The budget carrier, wholly owned by Virgin Australia Holdings, had cancelled flights on Thursday and put Friday's flights under review after Indonesia revoked its permission to fly due to a bureaucratic technicality.
"After consultation with the Indonesian Government, Tigerair Australia has been granted permission to operate flights from Bali to Australia until Monday 16 January 2017 to enable Australians who are currently in Bali to return home," Tigerair said in a statement.
"As a result of these services, Tigerair Australia will be able to bring around 2,000 customers back to Australia."
Tigerair flights from Melbourne, Adelaide and Perth to Bali which began last March are flying under Virgin Australia's licence and using its pilots until Indonesia grants approvals for Tigerair to operate them on its own.
Virgin Australia had previously operated the flights itself but shifted them to low-cost arm Tigerair in an attempt to restore its international division to profitability.
While Tigerair did not give details about the new administrative requirements, a source familiar with the matter said Indonesia earlier this week changed the agency that oversees Tigerair's operations.
Authority was taken from the department that dealt with regularly scheduled flights and switched to the department that handles charter operations, meaning more stringent sales requirements, said the source who was not authorised to speak publicly about the matter.
"(Tigerair) did not meet the rule for chartered flights. They should not sell tickets in the territories of Indonesia," Agoes Soebagio, a spokesman for air transport at the Indonesian ministry, said.
Tigerair Chief Executive Rob Sharp had earlier appealed to the Indonesian government to offer the airline a grace period to operate flights while it worked through the new requirements.
"If the Indonesian government does not wish to honor the current agreement, we are asking them to give us a grace period so that we can continue to fly while we work through the new requirements together," he said in a statement.
"This would help us to support our customers who make an important contribution to tourism in Indonesia."
Bali, which is known for its beaches, mountains and paddy fields, is a popular holiday destination for Australians.
Tiger said that flights to Australia from Bali from Tuesday 17 January onwards were under review and cancelled flights from Australia to Bali from Jan 13-20. Flights from Australia to Bali from Jan 21 onwards were also under review, it said in the statement.