The Academy Award-nominated actor received unspecified minor injuries in the accident, which happened last Friday in Washington DC.
Sinise's spokesperson Staci Wolfe confirmed to The AP that he had been forced to cancel a number of shows with Lt Dan Band as a result, saying that he was a passenger in the car.
Lt Dan Band were due to perform a fundraising show in Martinsville, Virginia last weekend. It is believed that this show will be rescheduled to take place at a later date.
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A second concert in the Californian city of Palm Desert, which was due to take place at the McCallum Theatre next weekend, has been cancelled.
Jim Hummer, who is executive director of the intended beneficiaries College of the Desert Foundation, told Palm Desert Patch that he was "relieved to hear that Mr Sinise wasn't seriously injured".
It has been confirmed that Sinise's injuries will not affect the production schedule of CSI: NY, which has already concluded filming for the current season.
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