The incident took place around 10:45 local time (15:45 GMT) in Hingham, about 13 miles (20 km) south of Boston.
Images from the scene show a gaping hole in the store’s glass front.
Authorities are investigating the cause of the accident.
The area in front of the store – part of a local shopping plaza – has been cordoned off by emergency personnel.
“The dark colour SUV went through at a rate of speed undetermined through a glass window and struck multiple people,” police chief Dave Jones told reporters on Monday.
It is unclear how many people were in the store at the time, though officials noted it happened just days before Thanksgiving in the US and during a busy holiday shopping season.
Bystanders helped treat some of the victims at the scene, officials said.
Hospital officials said some of the people brought in were severely hurt, a few with life-threatening injuries and some who could lose limbs.
Little is known about the male driver of the vehicle but authorities said he has not been taken to hospital and is speaking with police.
Police did not give any further information about the driver, including his age or any other identification.
They said the inquiry is still in a very preliminary stage, with District Attorney for Plymouth County Tim Cruz calling it an “active criminal investigation”.
“This is a terrible event and a terrible day,” he said.
Witnesses described the breaking glass as sounding like “an explosion” to local media.
Frank O’Brien, who was shopping nearby at time, told the Patriot-Ledger that the vehicle would had to have been travelling quickly to end up where it did.
“You’d have to really be picking up speed to end up in the storage area at the back side of the Apple store,” he said.