The incident allegedly happened on flight 1354 from Washington, D.C., to Boston, according to Boston ABC affiliate WCVB.
"On June 20, the crew of flight 1354 were notified of an incident between customers shortly before landing in Boston," JetBlue said in a statement. "The aircraft landed at approximately 11 p.m. local time where it was met by local authorities."
A woman on the flight accused Andrew Baker, known as A.J., of inappropriate touching, WCVB reported.
"A.J. is fully cooperating and looks forward to a resolution of this matter," Baker's attorney Roberto Braceras said in a statement to ABC News.
The U.S. Attorney's Office, which would usually have jurisdiction on a case happening on a plane, said it could not "confirm nor deny they are investigating" this case.
The Massachusetts State Police said the "matter is being handled by the US Attorney’s Office."
The governor's office deferred comment, saying only, "This is a personal matter for the Baker Family and A.J. will cooperate with any request from authorities."
Baker, a Republican, took over as governor of Massachusetts in January 2015. He ran against Democrat Deval Patrick in 2010, but lost, before beating Martha Coakley in 2014. The 61-year-old is running for reelection this year.
A.J. is one of the governor's three children, two boys and a girl.
ABC News' Rex Sakamoto, Devin Villacis and Brendan Rand contributed to this report.