Perry, 68, collapsed in his dressing room after he left the stage, TMZ reported.
Paramedics called to the scene put a tube down the Aerosmith rocker's throat to clear his air path, gave him oxygen and took him to a hospital.
The New York Daily News said Perry's representatives did not immediately respond to a request for comment and his condition remains unknown.
Neither Perry's nor Joel's Twitter feeds have mentioned the reported health crisis.
Perry's most recent post was a photo of him and Joel.