The band have already rescheduled their May 10 and 11 gigs at the Winstar Casino in Thackerville, Oklahoma for September 13 and 14, but have had to cancel six further dates.
All of their shows from the May 15 gig at the Blue Cross Arena in Rochester, New York to the May 22 concert at Colisee Pepsi Arena in Quebec City, Canada will not go ahead and will not be rescheduled.
Barker's recovery period from the tonsillectomy is expected to extend beyond the band's scheduled tour dates, their official website has announced.
However, there has been no confirmation on whether their UK and Ireland shows this July have been cancelled or rescheduled.
Blink-182's upcoming UK tour has already been rescheduled once before. The shows were originally due to take place across summer 2011 and were moved back a year.
The band have been touring their sixth studio album Neighborhoods, which reached number six in the UK and two in the US.
Watch the music video for Blink-182's 'After Midnight' below: