The computers were taken during a break-in at Swan Films in Rusholme, Manchester on Thursday afternoon.
The Crown Prosecution Service (CPS) said the computers had since been recovered and the video files had not been accessed. It has launched a review into its security arrangements.
Six men have been arrested in relation to the burglary.
A CPS spokeswoman said the material, which related to Greater Manchester Police cases and also included witnesses' video statements, was sent to the company in August.
"The CPS has secured all material which remained at the burgled premises and is asking for an urgent explanation of the security measures in place," she said.
She added staff had contacted those involved in the cases affected to inform them "of the successful recovery of the material in question".
Computers containing police interviews with victims have been stolen in a burglary at a video-editing contractor.