The Gallagher Premiership club said the 34-year-old will provide loosehead prop cover while Ben Harris and Tom West recover from injuries and Robin Hislop is away with Scotland.
Ex-Glasgow and London Irish forward Reid won 41 Test caps between 2014 and 2019, and he has been playing for Scottish Premiership club Marr this season.
Wasps head coach Lee Blackett said: “We are very happy to bring in someone of Gordon’s experience as short-term cover for us. Gordon will be vital for us, while we are without Ben and Westy and while Bomber could be away with Scotland.
“He has played a lot of games at the highest level, and as an experienced prop he will bring a lot to our scrum.”
Former Glasgow Warrior Reid joined up with Marr, based in Troon, during the summer from nearby Super6 side Ayrshire Bulldogs.