The officers had been called to the Subway store on Centurian Way at 11pm last night, spotting a vehicle leaving the scene.
The officers' car and the Seat Leon crashed, West Yorkshire Police has said, with four men fleeing the scene.
Police said two officers suffered minor injuries and a cash till, taken in the burglary, has since been recovered.
A 23-year-old man has been arrested in connection with the incident and remains in police custody this afternoon (Saturday).
Any witnesses are asked to call Huddersfield CID on 101 quoting 13180019991.