Tyler broke his left shoulder and needed 20 stitches in his head.
The statement said doctors have advised Tyler to take the time to properly recuperate from his injuries.
"Words can't express the sadness I feel for having to cancel this tour," guitarist Joe Perry said in the statement.
Perry said he wanted to thank the band's loyal fans for sticking by them, adding that the band hopes "we can get the Aerosmith machine up and running again as soon as possible."
The statement said ticket refunds for the remaining tour dates will be available at the place of purchase.
Earlier Thursday, Tyler released a lengthy statement thanking the Sturgis, S.D., police department and others who helped him after the fall. The 61-year-old also thanked the band's crew, the helicopter that evacuated him "for getting me outta there before I bled to death" and the doctors and nurses who treated him.
Tyler said thunderstorms delayed the band's set by an hour, then fuses blew and the audio systems failed shortly after the concert began.
"Well, I wasn't gonna go hide under the big top and play 'ROCK STAR' and wait for everything to be fixed," Tyler said. "I wanted to go out to the crowd to continue the show."
He said he was doing "the Tyler shuffle" when he slipped and fell off the edge of the stage.
"I just want to say that I' m plain grateful that I didn't break my neck," he said. "In truth, after thousands of live shows, falling off the edge four times ain't too bad."
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