The fire, which police believe was begun by the thieves in an attempt to erase any evidence and cause a distraction while they robbed the bank, broke out at around 6:15 am theTagesspiegel regional paper reported.
The thieves had smashed through reinforced concrete to dig their tunnel, meaning they must have had access to heavy duty equipment.
Police were still examining the scene in the Steglitz area of the capital on Monday afternoon and are yet to have found any clues pointing to suspects, despite thorough questioning of people living in the area.
Exactly how much money was stolen from the Volksbank branch has not been revealed and police said they had no idea where the ground excavated from the tunnel had ended up.
A similar incident took place in the southern part of Berlin in 1995, when an 11-strong gang tunnelled into a bank in Zehlendorf and took 16 hostages as well as several million euros.