An investigation has been launched following the incidents in Waterloo Terrace and Salop Street.
Firefighters from the town were first called to Waterloo Terrace shortly before midnight to reports of a small amount of refuse alight outside Cancer Research UK.
They used water to douse it.
A crew from Much Wenlock was sent to assist in Bridgnorth at this incident.
Then at 12.43am today the Bridgnorth crew was again called out to tackle a fire involving cardboard and a fence, in Salop Street – also in Bridgnorth where residents used buckets of water to put out the flames.
West Mercia Police also attended this incident.
Salop Street resident Elizabeth Worrall, 37, said: "At about 12.20 I woke up and smelled burning. I woke up my partner Phil and we both went downstairs to see what was going on. There was a fire at next door's fence which was about 10 yards from our door.
"Rob from the Bell &Talbot was outside as well. He and Phil picked up some buckets of water that were in the yard and started chucking water over the fire. The police drove past and said there had been another fire in the town. The brigade came about 20 minutes later.
"It's a bit worrying because it wasn't an accident. Someone has done this on purpose and the outcome could have been very different."
In a Facebook post Bridgnorth Fire Station stated: "At 23:55 we were alerted to a property fire at the Cancer Research Shop on Waterloo Terrace, High Street.
"On arrival we found a large amount of cardboard recycling alight up against the shop window. Crews were able to quickly remove the burning cardboard to save the window and shop, while extinguishing the fire with a hose reel jet.
"While there we were made (aware) by a police officer of a second fire located on Salop Street.
"We then attended this incident and located a fire again of recycling materials against a large wooden garage door. A hose reel jet was used again to extinguish the fire.
"Both incidents are being treated as arson and the police are investigating. If you have information or CCTV in the areas please phone 101 and report them."
Shropshire Fire & Rescue Service posted about the incidents on social media network Twitter.
Atb23.55hrs @SFRS_Bridgnorth were called to a quantity of rubbish set on fire in Waterloo Terrace Bridgnorth, a short time later at 00.44hrs they attended a report of cardboard & recycling set on fire in Salop St. Phone @BridgnorthCops on 101 or @CrimestoppersUK 0800555111 pic.twitter.com/aA0CrvVPh5— Shropshire Fire and Rescue Service (@shropsfire) October 13, 2020
Meanwhile in Wellington, Telford, crews were called to a property, in Clun Close, after two sheds accidentally caught fire at about 11.30pm last night.