"We got a tip-off that a number of explosive devices were to be detonated in Malmö and at the same time we were also alerted to the bank robbery, which was soon followed by a new alert and an explosive device outside the police station," said police spokeswoman Ewa-Gun Westford.
"We think the car explosion was a diversionary maneuvre for the bank robbery. That's our hypothesis but we are also open to other possibilities," she added.
A city centre pre-school was evacuated early in morning after a car bomb exploded outside the premises.
The car belonged to a parent who had just dropped a child off at the daycare centre on Carl Gustafs Väg, Skånska Dagbladet reports.
Police later confirmed that an explosive device had been placed under the rear section of the vehicle.
A bomb squad dispatched to the scene was observed checking the undersides of other vehicles parked in the area.
Shortly before lunch time, two armed robbers raided a branch of Handelsbanken in the Jägersro area on the southeastern edge of the city.
A car was discovered in flames on the other side of the E6 motorway in nearby Oxie.
Police could not say whether the burning car was in any way connected the robbery.
There have been no reports of any injuries in either the bank robbery or the car bomb incidents.
A few blocks north of the city centre, the police station at Porslinsgatan was sealed of at lunch time after the discovery of a suspicious bag.
The old police station at Davidshallstorg has also been cordoned off.
Police from the entire Skåne region have been called in to Malmö, where they have been requested to patrol the streets in the city centre during the afternoon and evening.