The stores in Yonkers, New Rochelle, Thornwood (Mount Pleasant) and Bedford Hills remain open.
Store officials said on Facebook any other employee who had contact with the affected employee is on a 14-day self-quarantine.
"We have implemented the Centers for Disease Control (CDC) recommended protocol to reduce the spread of the virus," store officials said.
Those steps include requiring the self-quarantine of employees who came in contact for a "prolonged" period of time and have sanitized all workspaces used by the associate and the common areas.
Store officials did not comment on whether the employees had any contact with customers.
Company officials are also asking customers to follow the same CDC guidelines and refrain from shopping in the supermarkets if they are sick, to cover any coughs or sneezes, and to practice social distancing.
"The containment of the Coronavirus is a shared responsibility," the Bedford Hills store said on Facebook. "We are proud of the amazing dedication our associates are demonstrating and we thank them for their service to our customers. Please join us in wishing our associate well and a speedy recovery."
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