A man in his 70s and a staff member have tested positive at Juniper's Cygnet residential care home in the Perth suburb of Bentley.
The home, which accommodates people living with dementia, has been indefinitely closed to all visitors but residents are not being confined to their rooms.
Juniper chief executive Chris Hall says the infected resident, who is isolating, is symptomatic but "doing really well".
Of the facility's 40 residents, 38 are triple-vaccinated, one is double-dosed and arrangements are being made to vaccinate one person who is yet to be jabbed.
"The first point at this stage is to really understand how the virus has got into the facility. The source of it is unknown," Mr Hall told ABC radio on Thursday.
"Once we have that understanding, that'll help us in terms of working the plan moving forward. We're confident that we'll get on top of this very quickly."
At this stage, no other staff members have been deemed to be close contacts.
WA Health reported 94 new cases on Wednesday, 14 locally acquired and the rest linked to interstate and overseas travellers.
The surge in travel-related cases came after the McGowan government softened its hard border rules, allowing more people to reunite with families.
More than 17,500 people have arrived in WA over the past four days with a requirement to self-quarantine for seven days and get tested.
Chief Health Officer Andy Robertson warned this week that local case numbers were expected to double every few days, but WA's tally has more than halved from the 31 infections reported on Sunday.
Health Minister Amber-Jade Sanderson said the numbers were lower than expected but warned the government expected a "very steep spike" in coming days.
"Certainly my suspicion is that people are just not getting tested," she told reporters.
"Based on the numbers that are coming through at the moment, we think there's more community transmission out there than is being reported."
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