The Scotstoun side cancelled training on Tuesday as a result of the case but are now preparing for their trip to Swansea on Saturday.
A club statement read: “Glasgow Warriors can confirm a squad player has tested positive for Covid-19.
“This was identified through the club’s stringent screening and testing protocol and the player started self-isolation immediately as per Scottish Government guidelines.
“Public Health Scotland’s contact tracing subsequently identified two other players who had close contact within the squad bubble and are also isolating.”
The club statement added: “The club continue to operate an extensive health and safety coronavirus mitigation plan and follow all respective public health guidance aligned through Scottish Rugby's Threat Management Group. To respect medical confidentiality Glasgow Warriors will not name the individuals affected.”
Glasgow have played twice so far this season, losing to Connacht and beating Scarlets.