Delta said it happened Tuesday night on Flight 1102 from Orlando to Boston.
An airline spokesperson said an off-duty police officer subdued the passenger, 43-year-old Robert Hersey of Massachusetts, and sat with him for the remainder of the flight that landed safely.
A spokesman from Logan International Airport said it was unclear why Hersey tried to open the door.
One passenger said the man was upset and intoxicated before boarding the plane in Orlando.
"He was kind of getting angry because the flight got delayed, and I know he was drinking because he asked me to go to the bar with him," said passenger Todd Varley.
The man is charged with interfering with a flight crew. He was scheduled to be arraigned Wednesday.
The Associated Press contributed to this report.