The cases have been isolated and have not impacted operational activities, the Ministry of Defence has said.
Those on the base have had access to twice-weekly lateral flow testing since February. The MoD said all Scottish Government guidelines have been complied with.
Some foreign air crews have entered the UK at RAF Lossiemouth but have not been required to self-isolate or take any Covid tests other than the twice-weekly lateral flow tests on offer to all staff.
Scottish Government guidelines include an exemption for military personnel for these requirements.
Visiting German personnel have been staying in local civilian hotels.
The MoD said the visiting crews aim to “minimise contact with the local community”, but the use of local hotels provides “welcome economic relief for our local hospitality sector”.
In response to queries from locals about the risks of arrivals from abroad into the local community without self-isolation via Lossiemouth, NHS Grampian said the cases were “just one setting” where Covid-19 was spread, and that it is impossible to pinpoint a single cause of the rise in cases.
An MoD spokesperson said: “RAF Lossiemouth currently has a small number of Covid positive cases in the work force, which have been identified through the robust asymptomatic testing that has been taking place on site since February 2021.
"All working at RAF Lossiemouth can participate in this testing twice weekly. RAF Lossiemouth also complies fully with all Scottish Government Covid regulations and policy."
The spokesperson added: “Our visiting German colleagues are fully compliant with Scottish Government regulations on international travel. They are participating in regular asymptomatic testing whilst working from RAF Lossiemouth and, noting the surge in local cases in Moray, are working hard to ensure they minimise all contact with the local community.”
The confirmation of cases comes as NHS Grampian praised locals for their response to the outbreak in Moray.
Around 50 per cent of those aged 18 to 29, and 60 per cent of those aged 30 to 49, have now been given a first dose of vaccine.
Chris Littlejohn, deputy director of public health, said there was cause for “cautious optimism” as case rates begin to reduce.