The robbers set off an explosive at 3am outside a branch of the Sparkasse bank in an attempt to break into a cash machine. But they were interrupted by officers, a police spokesman said.
Unwilling to come out quietly, the criminals opened fire without warning, the spokesman added.
A gunfight ensued, and though no police officers were injured, the robbers were able to make their escape in a dark-coloured car, taking the Bundesstraße 1.
Though the officers took off in pursuit, they lost the car in the darkness. A helicopter with a thermal imaging device also failed to track down the robbers, and investigators do not know the car’s make or model.
A nationwide manhunt is now under way, with police making a call for witnesses who may have seen the car fleeing on a motorway in the early hours, to come forward.
The bank was severely damaged by the explosion, and it remains unclear whether the bank robbers managed to escape with any loot.