An eyewitness said they saw the victim swimming off the shore of Bailey Island when she was attacked in the water.
Two kayakers brought the woman to shore but she was pronounced dead at the scene, according to the state’s Marine Patrol.
The authority is urging swimmers to exercise caution in the area and avoid swimming near schools of fish or seals.
It is only the second time in nearly 200 years that a shark attack has taken place in Maine, researchers at the Florida Museum of Natural History reported.
It is unclear whether the 1837 attack was fatal.
Attacks in the northeast of the US are generally rare, with New York State and Massachusetts logging 18 between them, according to the database which tracks shark activity worldwide.
Florida has recorded 852 attacks – the most in the world.
