Jim Peters, a spokesman for the Federal Aviation Administration, said the three were on board the single engine plane when it went down in the parking lot at Hannaford's grocery store at about 10:15 a.m. on Tuesday.
He had no further details.
Store manager Arthur Dechellis said he heard an explosion, and when he looked outside a two-seat plane was on fire. He said the plane crashed in an area of the parking lot where people rarely park and no cars were hit.
Dechellis said the store remained open and customers were going in and out.
Ashmita Kohli, an employee of a Quizno's in the plaza, told CBS station WBZ she saw at least one body at the scene.
"You could hear a plane then a big boom," she said. "It looks like a movie set right now."
Khol said the plane was engulfed in flames.
Mansfield Airport is located nearby. Officials there had no comment.
The plaza is home to Hannford's, Quizno's, as well as Target and T.J. Maxx department stores.