All players and staff are currently isolating as per Scottish Government guidelines, and have been in enforced self-isolation since travelling back from Leicester on Sunday (27 June). To respect medical confidentiality, Scottish Rugby will not name the individuals affected.
At this stage, Scottish Rugby has every intention of fulfilling the following week's international fixture against Georgia in Tbilisi (Saturday 17 July), however the current situation remains fluid and that match is subject to review and further testing.
As the non-positive players and staff leave isolation in the coming week, they will be subject to further medical assessment and testing prior to returning to a graduated training regime. Scottish Rugby will provide further updates in due course.
Scottish Rugby Chief Executive, Mark Dodson, said: "Player welfare is paramount in every decision that we make as an organisation, and unfortunately we've ran out of time to allow our players to recover and train properly for the Romania fixture.
"We're clearly disappointed, and I feel massively for both our group of players and management, as well the Romanian Rugby Federation, however our squad's health and wellbeing must come first.
"We still have every intention of travelling to face Georgia the following week, subject to further medical review and testing, and we'll hopefully be in a position where a large section of the squad will be able to return to a graduated training regime next week.
Scottish Rugby Chief Medical Officer, Dr James Robson said: "We unfortunately now have a situation where we have several COVID-19 positive cases within the playing group and management, and as such we've made the correct decision to call off the Romania fixture.
"Simply put, you cannot hurry players or management out of isolation, and with the health and wellbeing of the squad very much in mind, we wouldn't be in a position where we could safely travel to Romania and fulfil an international fixture.
"We'll now work intently on ensuring the squad and management are able to safely return to a graduated training regime."
Scotland Interim Head Coach Mike Blair said: "As a camp - of both management and players - we're obviously massively disappointed that we'll be unable to travel and face Romania next weekend, however it is 100 per cent the correct decision, taking into account the health and wellbeing of this group.
"It's clearly been a disappointing couple of days, however, since meeting as a squad over a fortnight ago, the determination and resilience shown by this group has been evident to see, and we'll move forward with that Georgia fixture very much in focus.
"We'll continue to work closely with Dr James Robson and the medical team at Scottish Rugby, who will advise and direct us as we look to return to a graduated training schedule in the coming week.
Scottish Rugby continues to operate an extensive health and safety coronavirus mitigation plan and follow all respective health guidance aligned through Scottish Rugby's Threat Management Group.