A player from Inverness Caledonian Thistle and another from Stenhousemuir are in self-isolation after showing symptoms associated with coronavirus.
The Scottish Championship club are awaiting the results of tests on the unidentified player, who did not train with the rest of the squad on Friday.
League Two Stenhousemuir said a squad member did not take part in a session on Thursday after feeling unwell.
There have not yet been any confirmed cases in Scottish football.
However, all matches were postponed earlier on Friday amid the outbreak, with SPFL chief executive Neil Doncaster saying it was "neither realistic nor possible" to continue with games.
All domestic professional and grassroots football under the jurisdiction of the Scottish FA has been suspended, including the Scottish Women's Premier League.
The move came after the UK government escalated its response and First Minister Nicola Sturgeon advised events of more than 500 people should be cancelled.