Both staff members at the High Street chain, which has only just reopened after lockdown, were said to have been asymptomatic prior to testing positive.
Both are currently self-isolating.
A spokesman for the pizza chain said they have been liaising with Public Health England.
He added: “The significant protocols we put in place ahead of our reopening meant that we were able to identify and isolate this issue quickly.”
Public Health England said it advised the restaurant on safety measures to protect customers and staff.
Public health consultant Dr Maha Saeed said: “We are working with Pizza Express and Kent County Council to provide public health advice and help stop the spread of the virus.
“Businesses, including restaurants and pubs, have been asked to take certain measures to help reduce the spread of Covid-19, including ensuring staff can maintain social distancing wherever possible and are able to regularly wash their hands for 20 seconds with soap and water, and cleaning frequently touched surfaces.”
