The airline says the discount will make it easier for residents moving to temporary lodgings outside the region, and also help people who are traveling to the region to contribute to the recovery effort.
ANA is requesting that people not use the discounted fares for holiday purposes.
The airline says the flat rate represents a cut of up to 70 percent on regular prices.
To qualify for the 10,000-yen fare, flyers have to choose the ANA VALUE option, which requires purchasing tickets at least one day in advance on the ANA website.
The airline is currently operating three round-trip flights per week between the two airports and will continue to do so until March 28.