The Dons' clash at McDiarmid Park on Saturday looked to have been given the go ahead on Wednesday despite First Minister Nicola Sturgeon reimposing strict lockdown measures on the city following a new outbreak.
But now McInnes and his squad face a nervous wait to learn if they will be allowed to travel to Perth.
In a statement given to the PA news agency, a club spokesperson said: "We have had a positive test but we are awaiting further guidance from Scottish government and the joint response group."
The player has been ordered to self-isolate after contracting the virus, while the rest of McInnes' squad was stood down from training on Thursday.
Sturgeon took the decision to impose new lockdown measures after 54 cases were reported in the city – with an additional 25 having since been discovered.
The cluster is linked to a number of bars and reports have claimed several members of McInnes' squad were spotted in city centre hotspots following Saturday's Pittodrie defeat to Rangers.
The new restrictions have ordered pubs, cafes and restaurants to close with five mile travel limits put in place.
As the Aberdeen squad were operating in a 'biosecure bubble' at their Cormack Park training base with twice weekly testing, it was expected they would be able to make the trip to take on Saints this weekend.
But that was before news of the positive test emerged and it remains to be seen if the game will go ahead.
An Aberdeen player tested positive last month before the top flight resumed and is the only player to have returned a positive test since training resumed – although McInnes later suggested it had been a false positive.