Interim chief executive Greg Pullen said the results for the remaining about 60 Maculata Place residents were expected on Tuesday.
"There is nothing sinister in the flow of results, it is simply the process which is out of our control," Mr Pullen said.
All 19 Bertram House residents have returned negative results at the weekend.
Mr Pullen said the resident who tested positive was the only person at Shepparton Villages who had shown COVID-19 symptoms, and had the test fast-tracked accordingly.
He said the resident was in "quite good" health given the diagnosis, and was being cared for on each shift by one particular person.
"So there's no crossover there (with other residents)," Mr Pullen said.
All staff have been required to wear full personal protective equipment, including a mask, face shield, gowns, and gloves.
All residents are in isolation and are having their health and temperature checked multiple times a day.
"We believe the residents are as safe in Maculata Place as they’d be anywhere because of all the precautions taken," he said.
Mr Pullen said most residents and relatives were "coping very well".
"We've been communicating with all relatives and keeping them in the loop, and I think they've appreciated that," he said.
"We'll continue doing so."
The precautions come after two Shepparton Villages staff members tested positive for the virus, which has also forced other staff members into isolation.
"We have 22 staff who are classified as close contacts who are self-isolating for 14 days regardless of the result, and need to be away from work for 14 days," Mr Pullen said.
"They'll be tested a couple of days before they start back at work."
While the first staff member who tested positive for COVID-19 had worked at Bertram House and Maculata Place while infectious, the second staff member was believed not to be infectious when at work.
"It is known that the second staff member is an acquaintance of the first staff member, and they were studying together," Mr Pullen said.
"So it is our belief is that (the transmission) happened outside of the the work situation."
Mr Pullen said there would be a second phase of tests for all Maculata Place residents on Thursday, August 13, and all would remain isolated until the second round of results were returned.
He said staff was following infection control protocols and the Emergency Management Plan, supported by GV Health and the COVID-19 case management team.
Goulburn Valley Health chief executive Matt Sharp said GV Health had been providing support to Shepparton Villages.
"GV Health has provided services which include contact tracing, specialist residential aged care in-reach, infection prevention and control," Mr Sharp said.
"In addition, nursing staff are working onsite at Maculata Place today."
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