Rovers are awaiting the results of a PCR test to know the fate of the on loan Arsenal midfielder, who missed Tuesday night's trip to Walsall in the Carabao Cup as a result.
Also missing the tie was Charlie Seaman, who car shares with Smith and would be required to isolate if the 20-year-old tests positive.
Boss Richie Wellens said: "Matt Smith has got a suspected Covid case.
"He drives in with Charlie Seaman so he's a possible close contact.
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"We'll have to wait for the PCR test on Wednesday.
"It's just what it's going to be like. It's demoralising.
"I just want to get cohesion. I think you saw signs of it tonight that the cohesion was there."
Rovers have seen three players test positive for Covid-19 since the return to pre-season training while many other senior players have been forced to self-isolate as a result of close contact.
Tommy Rowe was also absent from the squad at Walsall and Wellens admitted it was a case of not wanting to risk the veteran's fitness.
He said: "Tommy Rowe has got an enflamed Achilles tendon so there was no point in risking him.
"We'll see how he is on Wednesday.
"John Bostock has got a sore groin so we'll be in on Wednesday making sure everyone is all right."
Bostock was taken off during the second half after pulling up with an injury.