Boston College has played 77 times at the venerable ballpark, with the most recent game a 19-16 loss to Notre Dame in 2015.
It will be UConn's first game at the historic home field of the Boston Red Sox.
"I think this is a great opportunity for our team, to play a quality opponent, New England rival and in such a unique and famous setting," Huskies coach Randy Edsall said.
The 59th meeting between the schools will take place on Nov. 11.
"To be able to play a college football game at Fenway Park, where all the history and tradition is so rich, we could not be more excited about this opportunity for our program and fan base," Maine coach Joe Harasymiak said.
Maine has won the last two meetings with UMass, including a 24-14 victory in 2013 for just its second-ever victory over an FBS opponent. The programs previously played together in the Yankee Conference and the Atlantic 10 as well as the Colonial Athletic Association, where the Black Bears currently reside.
The Associated Press contributed to this report.