The health unit says it was notified of a case a week ago and received reports of two additional cases among staff on Friday.
The store has been closed since Oct. 11, after the first staff member tested positive.
Investigations determined that two of the three staff members worked while they were infectious, the health unit said in a statement.
The MLHU has determined that transmission of COVID-19 has occurred at the store.
“We know many people visit Starbucks frequently and that this news may cause concern, but I want to be clear that the risk of contracting COVID-19 in a situation like this is very low,” said Dr. Chris Mackie, medical officer of health with the MLHU.
“Any interactions would have been brief and there was a physical barrier that would have reduced the possibility for COVID-19 transmission.”
The health unit advises customers who visited this Starbucks location on Oct. 3, 4, 6, 7 or 8 to monitor themselves for COVID-19 symptoms.