The newly renovated bridge has shifted sideways and risen 50 centimetres.
"Absolutely no one is allowed up on it," Joakim Kastemyr of the emergency services told the Aftonbladet newspaper.
The bridge will remain closed for some time due to the extent of the damage, according to the Swedish Transport Administration, with traffic being diverted away from the E45.
"It's going to take time to turn this back into a bridge again. You can see from the pictures that it has been severely impacted," Kastemyr told Aftonbladet.
Emergency services were alerted at around 11.30pm on Tuesday when a heavy special transport vehicle was driving across the bridge. The driver was able to exit the vehicle and safely get off the bridge, but the vehicle remains stranded there, according to Aftonbladet.
The 70-year-old Strömsund Bridge has undergone several stages of renovation over the past five years, partly to improve its capacity to handle heavy transport. Following the upgrades, vehicles weighing up to 74 tonnes were permitted to drive across the 332-metre-long bridge.