The 65-year-old Aerosmith guitarist staggered offstage minutes into the band's set at Brooklyn's Coney Island Boardwalk on Sunday (10Jul16), and was admitted to a nearby hospital.
Cooper and company cancelled a planned performance on U.S. chat show The Late Show With Stephen Colbert on Monday night (11Jul16), but none of their tour dates will be affected.
Cooper took to Twitter to confirm the band will continue with all dates, and will take the stage at Fraze Pavillion in Kettering, Ohio on Tuesday (12Jul16) as scheduled.
"We WILL see you in Ohio tomorrow night & for the rest of our dates!" Cooper wrote. "Thanks for supporting Joe!"
It is not known if Perry will be well enough to perform on Tuesday.
The band's tour is slated to end in Paso Robles, California on 25 July (16).
Meanwhile, Perry's Aerosmith bandmate Steven Tyler also took to Twitter on Monday to send his best wishes to the guitarist, writing, "I LOVE YOU @JOEPERRY...FEEL THE MILLIONS OF PRAYERS COMING YOUR WAY...WE ALL LOVE YOU...SENDING WHITE LIGHT AND ALL THAT I GOT YOUR WAY."