A West Yorkshire Fire and Rescue Service spokesperson said the suspects had been caught on CCTV and police were investigating the cause of the blaze.
Firefighters from Wakefield were called to Tesco Express, Stanley Road, at around 2.20am, where they found a bin storage area ablaze.
Watch commander Vinny Nickle, of Wakefield Fire Station, said: “It was fully involved when we got there, but it was limited to the rear area of the store and had not spread to the building.
“There was a wall which had stopped it spreading, but the fire did destroy some air cooling units which were in the same area.”
Crews used jets, hose reels to extinguish the fire and a thermal imaging camera to check for further fire hotspots.
The scene was cleared by around 4.15am.