The 37-year-old, who also starred in the revival of TV series "Dallas", was arrested at his home in the Los Angeles area, taken into custody and booked for burglary on Tuesday after his neighbours claimed they had surveillance footage showing Henderson and two other men stealing their valuable belongings.
According to TMZ.com, the neighbours returned to their home at the weekend to find around $7,000 worth of jewellery missing and told police officers they had surveillance footage capturing the crime and said they recognised Henderson as one of the culprits.
However, editors report that it might be a case of mistaken identity as the footage only showed three men in hoodies climbing over a balcony and making off with the items.
A source connected to the actor said, "Josh was initially mistakenly identified with a grainy security camera, but he is fully cooperating and evidence is now being presented to the authorities showing he had nothing to do with any of this. Josh is innocent and we are confident he will be cleared very quickly."
Investigators are currently reviewing the surveillance footage. Henderson was bailed out of custody on Tuesday.