The two courts trying Hasina, the head of the Awami League, ruled that the hearings could continue in her absence, allowing her to leave the country.
Hasina asked on Sunday for permission to allow lawyers to appear on her behalf in court, after a government-appointed medical board suggested she should be sent abroad immediately for treatment.
Hasina, who was prime minister from 1996-2001, is expected to travel to the US.
She was arrested in July by Bangladesh's new military-backed interim government and faces at least four graft charges.
Mukul said that Hasina could be released as early as Monday evening.
The government is attempting to ease tensions with the main political parties as they look to hold elections in December.
However, Begum Khaleda Zia, another former prime minister being also held on corruption charges, has accused the government of trying to set a trap by allowing the leaders to travel abroad.
The government could block Hasina or Zia's return were they to leave the county.
Zia said that she would not seek medical treatment abroad, despite a medical board saying that she should travel for treatment for arthritis and knee problems.