The video was recorded by a member of the public in Victoria Road West at around 10.05pm on Sunday, March 13.
Eyewitnesses said the fire started in the corner of the shelter before spreading to the roof and a nearby bin.
Residents believed the fire may have been started intentionally, but this has not yet been confirmed.
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However, Lancashire Police said the cause of the fire was under investigation.
"An insurance claim is being submitted to the council’s insurers with a view to reinstating the shelter,” a spokesman for the force added.
Two fire engines from Bispham and Fleetwood attended the scene.
Firefighters used two hose reel jets, one breathing apparatus, and one triple extension ladder to extinguish the flames.
Crews were in attendance for one and a half hours.
Wyre Council has been approached for comment.