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Seven coaches and backroom staff at St Mirren have tested positive for Covid-19, while Rangers face a probe into concerns of a possible testing breach.
Although no player has tested positive, the Paisley side's Saturday friendly at home to St Johnstone is now off.
The Scottish Professional Football League club is now on lockdown until more tests are carried out.
It has also emerged Rangers face an SFA probe into whether the club breached testing protocols.
The SFA want to know if Ibrox players, who took part in a game against Dundee United on Wednesday, had been given the necessary results in time.
Following the news from St Mirren Park, Premiership clubs have been ordered to revert to two Covid tests per week rather than one.
Scottish football's joint response group (JRG) said: "We immediately contacted the Scottish government and the office of the clinical director for Scotland to relay this information.
"In light of this and other recent events, the JRG hereby notifies Scottish Premiership clubs that with immediate effect they must revert to twice-weekly testing protocols until further notice."
St Mirren, who start their competitive campaign at home to Livingston on 1 August, last played Hamilton Academical in a friendly on Saturday.
Hamilton Academical said all players and backroom staff were tested two days after that match, with all returned results being negative.
A statement from the club said: "Following the departure of the St Mirren squad on Saturday, the area used was cleaned and disinfected.
"The location occupied by St Mirren was a segregated area at the far end of our stadium and is separate from the areas used by Hamilton Accies' players and staff on a matchday. Subsequently on Monday, all players and backroom staff were tested with all results returned negative.
"Hamilton Academical will continue to follow advice from the SFA/SPFL joint response group."
Meanwhile, Rangers' investigation relates to two friendly matches played on Wednesday.
Match delayed
Current rules state players cannot take part in any matches unless they have negative test results from weekly screenings.
The Ibrox club's friendly against Motherwell on Wednesday was delayed by two hours due to results being held up.
But, earlier that day, squad members took part in another closed doors match against Dundee United at the club's training centre.
The SFA is now looking to see if the players who took part in that game had the necessary results in time.
Motherwell and Hibs have also been asked to explain delayed results which have impacted matches.
Scottish football's governing body has already written to clubs reminding them of the importance of sticking to the rules ahead of the new season kicking off on 1 August.