The Dreamliners had been grounded for more than three months after reports of burning batteries on two Japanese planes.
The airlines were given the go-ahead to put the planes in the air Friday, beginning with test flights.
The ministry's decision came after a similar decision by the U.S. Federal Aviation Administration to let the 787 jet resume flying after approval of Boeing's modified battery system last week.
Other carriers around the world also were preparing to resume flights of the 787s at an early date.
All Nippon Airways and JAL, the world's two largest 787 operators, began installing the modified lithium-ion battery on their fleets and plan to conduct test flights before proceeding with commercial operations in June at the earliest, the report said.
Kyodo said Ethiopian Airlines expects to resume its 787 operations by Saturday. United Airlines, the only U.S. airline with 787s in its fleet, is looking to resume flights in late May.
The report said U.S. and Japanese aviation experts were still looking into the battery overheating incidents in what could be a yearlong investigation.
Japanese Transport Minister Akihiro Ota told a news conference Friday several measures have been taken to eliminate possible risks of fire, Kyodo said.
CNN reported nearly 50 Dreamliners around the world had been grounded.
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