"We only have so much testing capacity", she said, when asked Monday about the issue.
Eighteen people are now hospitalized and seven are in intensive care.
The woman lived in a longterm care facility. Eleven other residents are showing symptoms, Hinshaw said.
"I know there has been some concern expressed that our change in our strategy for testing means that there is a bunch of cases that we are actually not getting to or that we are not recognizing in the community", she told a media briefing.
Effective today, travellers who returned to the province after March 12 and have mild symptoms will no longer be tested for COVID-19.
"It's why these aggressive measures are in place", Hinshaw said, referring to the province's ban on mass gatherings, closure of rec centres, limitations on restaurant capacity and physical distancing rules.
The number of confirmed COVID-19 recoveries remains at three, and to date, one person has died in the province.
Team Canada will not compete in Tokyo 2020
Pound's revelation comes 24 hours after International Olympic Committee president Thomas Bach admitted that postponement was a realistic outcome.
Alberta now has 358 cases of the novel coronavirus.
One more COVID-19 patient is now in hospital increasing the total to 19, but the number of ICU cases remained at seven.
The Alberta government has added a temporary billing code to assure doctors are evenly paid for virtual visits.
Travellers coming back into the country will still be required to self-isolate for 14 days.
Anyone with symptoms who does not fit any of these categories should stay home and self-isolate for a minimum of 10 days from the start of their symptoms, or until symptoms resolve, whichever is longer. They will be met at the entrance and will have their temperature taken and will be asked to fill out a short questionnaire.
When they return, he says, they must go home directly to self-isolate and, if they need supplies, make arrangements to have them delivered by someone else.