The band's tour bus came to a sudden halt after a pedestrian walked in front of the vehicle in Boston, Massachusetts over the weekend (09-10Aug14).
Followill was hospitalised after the accident to treat a number of broken ribs, and doctors have advised him to stop work so he can recover.
The band has now axed nine concerts, including shows in New York, Ohio and New Hampshire.
Followill says, "I'm counting down the days until I can get back in the saddle and continue what has been our best American tour so far."
The group will resume the trek on 28 August (14) in New Jersey. They will go ahead with a planned performance on U.S. late night Tv programme The Tonight Show Starring Jimmy Fallon on Wednesday (13Aug14), with the show's resident band leader ?uestlove filling in for the injured drummer.