The van was delivering cash to the Heron Foods store on Harehills Lane, Harehills, when the raiders struck at about 12.25pm today.
They stole the guard’s cashbox – unaware that it contained no money – before driving off in a black car towards Cowper Road.
The incident took place to the rear of the store, on Cowper Mount.
All of the raiders were wearing either balaclavas or scarves across their faces.
One was carrying a red handled knife while another was wearing a black jacket with a yellow stripe on it.
Their getaway car is thought to have been a Ford Fiesta.
Leeds District CID’s Det Insp Richard Holmes said: “The victim received no injuries during the incident but was left understandably shaken by what happened.
“We are carrying out extensive enquiries into this offence and would like to hear from anyone who witnessed the incident or who saw the suspects or the vehicle in the area before the incident or escaping from the scene.
“The cashbox that was taken has not yet been recovered and we would like to hear from anyone who has found one abandoned in the vicinity or elsewhere.”
Anyone with information about the incident is asked to ring Leeds District CID via West Yorkshire Police’s 101 number or Crimestoppers anonymously on 0800 555111.