Southampton's Stuart Armstrong has returned a positive test, with the Scottish FA confirming Tierney, Celtic's Ryan Christie and two members of staff must isolate - starting from yesterday - after coming into close contact with the midfielder.
A statement said: "The Scottish FA has been informed that Stuart Armstrong has returned a positive test for COVID-19.
"The midfielder returned a negative test for COVID-19 on arrival at Oriam on Monday but the supplementary UEFA test returned a positive result this morning.
"Stuart will self-isolate for 10 days from the date of the test – Tuesday, 6 October - and will now be unavailable for the forthcoming international matches.
"All other members of the squad have returned negative results. However, the Lothian Health Protection Team have identified two players and two members of the backroom staff as close contacts.
"As a consequence, Kieran Tierney and Ryan Christie – along with one physiotherapist and one masseur - will require to self-isolate for 14 days as of yesterday, and will also miss the forthcoming matches."
Tierney's isolation will rule him out of Arsenal's Premier League trip to Manchester City on October 18.