This will be the first voyage of navy ship from Sri Lanka, as part of its Samudra Setu mission.
Earlier, three ships had evacuated around 1500 people from neighbouring Maldives.
Indian High Commission in Colombo has requested for support of Sri Lankan authorities in carrying out the evacuation exercise.
An Air India flight to Mumbai is scheduled for next Friday while more flights are being planned for evacuation.
The High Commission said priority will be given to compelling cases in distress including migrant workers who have been laid off, medical emergency, students and those suffering personal losses.
There are around 1,200 Indian nationals registered with Indian High Commission for evacuation due to COVID crisis and have been waiting for returning back home.
Around hundred of them are tourists who came for holiday for few days but got stuck due to stopping of international flights.
Indian nationals constitute the maximum number of tourists to the neighboring country.