The incident took place on Monday morning, when officers stopped a classic Volvo in Mona Street, Balby.
The driver tried to avoid officers, but was unsuccessful, but the front seat passenger managed to run away.
A significant number of police resources were sent out to the area, and officers explained the situation to the filming crew for Still Open Hours who were filming just two streets away on Lister Avenue with Sir David Jason and other cast members.
Shortly afterwards, crew members helped to detain the front seat passenger who was being pursued by officers.
A South Yorkshire Police said: “The film crew for #OpenAllHours were filming in the area and our officers had been talking to them earlier.
“Having heard the commotion of the sirens and seeing a bit of a chase the crew put two and two together when they saw the passenger running towards them so decided to intervene and detain the chap.
“Both males are in custody and have been arrested on suspicion of burglaries across the area and also for possession of class A drug. The investigation continues.”
It is not yet known whether Sir David Jason was nearby when the man was detained.