The collapse of a lighting rig in a pre-show set-up at Detroit's Pontiac Silverdome was cited as the cause.
Following the incident in Detroit, the Oscar-winning composer said he was forced to cancel the shows in Detroit and Toronto.
'The lighting rig came apart,' Rahman said in a statement. 'Thanks to the Almighty that everyone's safe. My team escaped with minor injuries. Dates in Detroit and Toronto will be rescheduled due to the incident.'
'I regret any inconvenience this causes my fans and am deeply grateful no one from my team or the local Detroit stage crew was seriously injured,' he added.
The concert tour got on to a rousing start in New York on June 11, continued in Atlantic City and Virginia. It will travel to over 20 major venues worldwide.
Image: A R Rahman at the Jai Ho Concert in Atlantic City, New Jersey. Photograph: Paresh Gandhi