According to a police official, the robbery may have taken place during the weekend holiday but came to light when the branch opened on Monday morning.
Investigators said the tunnel was dug from outside to the bank's store room which houses private lockers.
But the robbers could not break open the main safe vault housing the bank's cash reserves.
Bank Of Baroda officials declined to comment on the incident or the losses suffered by the branch. The bank losses were estimated by the police.