West Yorkshire Police said the accident happened on the southbound carriageway prior to junction 42 at 1.50pm and involved just one vehicle.
A police spokesman said there were no reports of any fatalities but air ambulances had been sent to the scene.
The occupants of the vehicle were said to be all suffering with "varying degree of injuries", the spokesman added.
He said: "At around 1.50pm we received numerous reports of a single vehicle road traffic collision which occurred on the M1 southbound just prior to junction 42 (M62 junction).
"I can confirm there are 12 casualties all from the minibus with varying degree of injuries. Although no fatalities at this time have been identified.
"I can confirm air ambulances are in attendance," he added.
All the casualties are men aged in their 20s and 30s and from the Rochdale area, a police spokeswoman confirmed.
She said seven men had serious injuries, while the other five were categorised as having minor injuries. They were taken to Leeds General Infirmary and Pinderfields Hospital in Wakefield.
Police said the minibus overturned on a grass verge on a slip road and officers are appealing for witnesses to the accident.
One lane on the southbound carriageway of the M1 was closed following the accident but reopened shortly before 4.30pm.
A slip-road onto the M62 remains closed.
The road closure is expected to be in place for two hours.