The rock band was supposed to return to the stage on August 28 for a show at the PNC Bank Arts Center in Holmdel, New Jersey, but that gig has been axed, along with August 29 concert at the First Niagara Pavilion in Pittsburgh, reported Rolling Stones magazine.
Refunds for fans will be available wherever they purchased tickets.
"After further evaluation, a doctor has ordered drummer Nathan Followill to remain on rest for one more week. The drummer has been on strict doctor's orders to rest over the past two weeks in order to recover from an injury sustained in a tour bus accident earlier this month," the band said in a statement.
"I'm so bummed to have to cancel more shows but I need to be fully recovered before I get back. So sorry to the fans and thanks for understanding," he tweeted.