The Flixbus vehicle toppled on its side around midday (1100 GMT) as it took an exit from the A1 motorway, France's busiest route, a police statement said.
There were 33 people on board, of whom 29 sustained light injuries and four were seriously wounded. Some of the injured were foreign nationals.
The statement did not say whether the bus was bound for London or for Paris. Rescue teams from the police, fire brigade, and ambulance service rushed to the scene.
The motorway exit has been closed, the statement said.
According to the newspaper “Courrier Picard”, the bus skidded in a curve on the wet road, crashed into a barrier and overturned.
It is yet another incident for the embattled German brand, with several crashes across Europe so far in 2019.
In October, one person was killed and 17 injured when a Flixbus rolled in Southern France.
Several people were injured in two separate crashes in Germany in June, while one person was killed and 60 injured in a crash in Switzerland in May.