Armed officers were seen on Whitburn Street and High Street in the town at about 1.30pm on Wednesday after the men fled the scene, abandoning their vehicle.
Offices nearby were evacuated, while those in the police cordon were told to stay indoors. The cordon was lifted at around 4.30pm.
It is believed a white Peugeot crashed with a car on Bridgnorth High Street and a building on Waterloo Terrace, before being found abandoned in East Castle Street.
Police are still trying to find the pair and launched an appeal for witnesses.
Inspector Paul Mathison from West Mercia Police said: " I would like to reassure the local community that they are in no danger and this is not in any way related to terrorism.
"I would also like to thank the public for their patience whilst officers carried out searches in the local area."
University student Ellen Walker, 20, said: "I saw two police cars outside the ice cream shop Knickerbockers in Low Town, then came up to High Town and saw all the police.
"I live right around the corner from Whitburn Street, you occasionally see a police officer, but I've never ever ever seen anything like this and I've lived here for 18 years.
"You don't see this in Bridgnorth at all, it's very shocking."
The manager of an estate agents, Berriman Eaton, based in Whitburn Street, was out at a meeting when the street was closed.
Bruce Attwood said: "I was out at a meeting but my colleague was told she has to stay in the office.
"Those at Terry Jones Solicitors have also been told to stay in their office.
"The police were here at 11.30am, before I went out, so they were there for at least two and a half hours with sniffer dogs.
"Someone said cars had smashed into each other.
"I've been working here for 15 years and I've never seen anything on this scale in Bridgnorth.
"It's quite shocking, especially with what's been going on in the country."
Members of the public were advised to call police if they see anyone behaving suspiciously in the area and are asked to call 101, quoting incident number 190s of June 7 if they witnessed the collision.
Reporter Jordan Reynolds was live at the scene
Residents are talking to the police for reassurance— Jordan Reynolds (@jreynolds_star) June 7, 2017
Armed police in helmets hammering on a door in Whitburn Street— Jordan Reynolds (@jreynolds_star) June 7, 2017
Police now shouting through the door "armed police you in the building come to the front door now"— Jordan Reynolds (@jreynolds_star) June 7, 2017
Bruce Attwood from Berriman Eaton estate agents said his colleague has been told she cannot leave the building.— Jordan Reynolds (@jreynolds_star) June 7, 2017
Residents are saying they've never seen anything like this in the town and that it is shocking— Jordan Reynolds (@jreynolds_star) June 7, 2017