According to a police official, the film style 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 an adjoining shop outside the bank's store room, which houses private lockers rented out to people for safekeeping of valuable and documents.
However, the robbers could not break open the main safe housing the bank's cash reserves.
The robbery - reminiscent of the British-Hollywood flick "The Bank Job" - created a sensation and hundreds of locals gathered there to see the unfolding drama.
A police official said it could be the work of expert criminals and a new modus operandi had been revealed which may need to be factored in by security agencies manning such banks.
"The thieves had rented out the adjoining shop since May 2017. The culprits have dug an underground tunnel of 25 feet long to the locker room of the bank," Navi Mumbai Police Commissioner Hemant Nagrale said in a brief statement.
He added that 30 of the bank safe's 225 lockers had been broken into and the robbers escaped with the loot, the value of which is yet to be ascertained.
Nagrale said the police had found some leads and teams of officers and men were working on them.
Though the loss could run into several crores of rupees, the process of assessment was still on. The bank had called all its customers and was verifying other records.
Despite repeated attempts, Bank Of Baroda officials declined to comment on the incident or the losses suffered by the branch.
The robbery came to light around 11 a.m. when a customer approached the bank to operate his locker and was escorted to the safe vault by a staffer.
They were shocked to see many lockers broken open and also the tunnel through which the thieves had entered and exited.
Preliminary investigation revealed the robbers had recced the area many times and were familiar with the construction and architecture of the bank as well the locker room.
They had also mapped the entire area and executed the crime with proper planning, keeping the entire neighbourhood in the dark.
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