Tierney will have to isolate for 14 days after international team-mate Stuart Armstrong tested positive for the virus, but in a statement, the Gunners confirmed the 23-year-old followed coronavirus protocol and are seeking further details on the situation.
"Our medical team have confirmed that Kieran was socially distant at all times from the player who tested positive and has broken no rules regarding COVID-19 protocols. We are currently seeking further advice and clarification of the details," read the statement.
Tierney - who is set to miss the game against Manchester City on October 18 - added: "I'm so disappointed and frustrated to be in this situation.
"I have adhered to all regulations and made sure I was socially distancing from my team-mates in the hotel. I've also tested negative.
"I know Arsenal and the SFA are now in discussions with the Scottish authorities to gain a further understanding."
Tierney, Celtic's Ryan Christie and two staff members started their 14-day self-isolation period yesterday, with a Scottish FA statement reading: "We have 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. "