Two men were taken to hospital for treatment following the incident in Gordon Street in the city centre on Sunday night.
It is understood one line of inquiry is that the attack involved a corrosive substance.
A Police Scotland spokesman said: “We were made aware of a disturbance involving a group of people on Gordon Street in Glasgow around 11.40pm on Sunday August 29.
“Two men were taken to hospital for treatment following the incident and inquiries are ongoing.
“Anyone with information can call 101, quoting 4659 of August 29.”
A message from the Editor:
Thank you for reading this article. We're more reliant on your support than ever as the shift in consumer habits brought about by coronavirus impacts our advertisers.
If you haven't already, please consider supporting our trusted, fact-checked journalism by taking out a digital subscription.