Bowmer and Kirkland staff are self-isolating and have been closed for a thorough cleaning.
The centre is structured at Summit Park in Sutton-in-Ashfield, Nottinghamshire.
Nottinghamshire County Council has shown that it is working in good physical condition and an incident team has been set up to deal with the outbreak.
Others affected by the outbreak paintings for site developers Peveril Securities and Sladen Estates.
A set of structured corporations in question said none of the positive staff members had been on site since Wednesday.
One spokeswoman said: “The fitness and protection of everyone on the site remains a more sensible priority, and we will follow our already rigorous hygiene practices.”
“We have selected to remove all agents from Thursday to carry out a thorough cleaning of the site in order to keep an environment running for everyone.
“We are working intensively with the public aptitude authority on the right next steps and we keep in touch with everyone involved.”
Corporations reported that a follow-up and procedure had met other staff members who were now quarantined as a precautionary measure.
Ashfield district council leader Jason Zadrozny said the authority working with Nottinghamshire companies and director of public aptitude “must ensure that the spread of the virus is contained.”
He added: “This is an evolving situation, and our environmental fitness team has video and is working with contractors and the protection and fitness manager to ensure that all protocols are strictly followed.
“While Summit Park is vital to the local economy, it is vital that government rules are strictly followed to prevent other cases.
Amazon said the site “has not yet been delivered” and that the distribution center is scheduled to officially open in the fall.
It is one of 3 sites created through Amazon that will create 7,000 jobs across the UK.
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