Both the Celtic midfielder and Arsenal left-back were instructed to quarantine for 14 days after their former Celtic team-mate, Stuart Armstrong, tested positive for Covid-19 while on international duty.
All three players will miss Scotland's crunch play-off match against Israel on Thursday evening, as well as the Nations League games against Slovakia on Sunday and Czech Republic next Wednesday.
Tierney has also been ruled out of Arsenal's next fixture against Manchester City while Christie is now set to miss the first Old Firm match of the season against Rangers on Saturday, October 17.
Both Celtic and Arsenal called for clarification from the Scottish authorities over the 14 day self-isolation period, however, professor Leitch insisted that footballers are treated the same as any other member of the public when it comes to Covid-19 protocols.
"The local health protection team in Lothian treats footballers the way it treats workers in call centres," he told Clyde One.
"We phone up the positive case, we ask them their history, where they have been for two days prior to their symptoms beginning.
"That's sometimes very straight forward, sometimes, particularly in football, it's slightly more complex, and then they make a judgement about who they've been in close contact with.
"The health protection team in Lothian have decided who the contacts are and those contacts have been asked to self-isolate.
"I cannot intervene or second guess what that process is. That's exactly how the process should work and footballers are not treated any differently in that bit of the process than any other member of our society."