The player returned the positive test on Tuesday and has been sent home to isolate.
Manager Poya Asbaghi said at his pre-match press conference on Wednesday that no other players have been infected following the latest round of lateral flow tests that each player took on Wednesday morning.
West Brom tried to get their Championship clash with Reading on Saturday postponed because four players had returned positive tests.
Albion were without Cedric Kipre, Semi Ajayi, Matt Clarke and Conor Townsend for the weekend’s win over Reading.
EFL rules say games must be fulfilled if clubs have 14 fit players available, although they leave it up to clubs to decide whether or not to call off matches.
Barnsley boss Asbaghi said: “We have ad one player return a positive test, he is now isolating.
“Our focus is on Friday, this is a special situation but I don’t know any more on West Brom.
“It’s been important even before this week that we don’t relax around Covid, so we follow the recommendations.
“Now that we’ve had one case it requires extra attention so we don’t let the virus spread.”