AP Photo/Nam Y. Huh
The plane was parked on the tarmac, with no passengers or crew on the plane, the Boston Globe reported.
Boston Fire Department spokesman Steve MacDonald said the fire was in the belly of the Japan Airlines aircraft, which flies between Tokyo and Boston.
The fire has been extinguished.
Boeing has been dealing with electrical issues in the Dreamliner in recent months: At least three airplanes were grounded in December due to problems in the planes' electrical distribution panel.
Also in December, the U.S. Federal Aviation Administration required that Boeing inspect its new 787s, after fuel leaks on two planes were reported.
Boeing CEO has dismissed such problems as "normal squawks."