In a statement released on Wednesday, the Coventry-based club announced that four unnamed players and three staff members had all returned positive tests following the latest round of the PCR screening programme.
Those seven individuals are now self-isolating in line with Government protocol, while those identified as "close contacts" are also having to isolate.
Wasps added that they have cancelled training for the rest of this week as an "added precautionary measure".
Lee Blackett's side are due to face Exeter Chiefs in their first Premiership Rugby Final appearance since 2017 at Twickenham on Saturday, October 24.
Wasps reached the season showpiece courtesy of a 47-24 win over Bristol Bears at the Ricoh Arena on Sunday, with tries from Dan Robson, Jack Willis, Zach Kibirige, Matteo Minozzi and Malakai Fekitoa and 22 points from the boot of Jimmy Gopperth.
Bristol are due to meet Toulon in the European Challenge Cup Final in Aix-en-Provence near Marseille on Friday evening and confirmed on Wednesday that all of their latest Covid-19 tests had come back negative ahead of their departure on Thursday.
Exeter, meanwhile, also face Racing 92 in the Heineken Champions Cup Final at Ashton Gate in Bristol on Saturday and similarly reported zero positive results from their latest round of coronavirus testing.