Youths strap hamster to firework
Officers believe the incident, which was recorded on a video phone, happened in the Possilpark area of the city recently.
The video clip showed the youths laughing before the incident and making sure they recorded the attack.
The Scottish Society for the Prevention of Cruelty to Animals said such crimes must be taken seriously.
A spokeswoman for Strathclyde Police told The Scottish Sun newspaper it had launched a search for those responsible for the "horrific" attack.
The police spokeswoman said: "We are aware of this horrific crime and inquiries are ongoing to determine the person and persons responsible."
During the video clip, one of the youths could be heard saying: "I'll hold it and someone else tape it."
Another youth urged a friend to put his phone on record mode so the prank could be saved.
After attaching the animal to the firework, one said "leave it like that, that's it", and another asked for a lighter before they set it off.
The youngsters were then heard laughing after the firework shot into the air and exploded.
The SSPCA said: "We received some information regarding this incident and we are working closely with Strathclyde Police.
"Any children carrying out an act like this need to be caught because it is not normal behaviour. It needs to be addressed and addressed quickly.
"It is important that people take animal cruelty seriously - it is often a warning of something much worse."