Positivity rates have climbed in the district to 114.8 per 100,000 people after the outbreak.
Some 104 cases have been confirmed.
Clipper would not confirm to the Yorkshire Post how many cases are directly linked to the warehouse, or how many staff are self-isolating, and have said there is no evidence anyone contracting covid while working at the warehouse.
Public Health England (PHE) have introduced extended testing in Selby in a bid to control the outbreak.
The site, on the town’s Barlby Road, is used to process returns for online superstore ASOS.
Community spread is also being monitored in order to control the spread of the disease.
Earlier this week, the TUC called for more to be done to protect staff at the warehouse while the outbreak is ongoing.
The site has not been told to close by PHE, and extra measures have been applied by Clipper including introducing staggered start times and maintaining social distancing.
But Clipper would not confirm to the Yorkshire Post how employees worried about coming to work while the outbreak is ongoing are being supported.
A spokesperson for the TUC said: "No-one should be forced to work in unsafe conditions. The local authority must urgently investigate this outbreak and take this employer to task.”
Louise Wallace, North Yorkshire’s Director of Public Health said: “This outbreak is a reminder that Covid-19 is still with us and can easily spread across our communities.
“All agencies in Selby are focused on how further infections can be stopped and the rates brought under control.
“I am grateful for all of the effort that has been put in by colleagues from our council as well as Selby District Council and other agencies to try and limit any spread and to make sure that businesses and other community organisations centred around Selby are on top of all of their precautions to avoid any further community transmission.
“Selby is geographically located at the heart of the wider Yorkshire region, with extensive transport networks and lots of inward and outward travel to work so its Covid-19 infection rate is prone to that sort of turbulence, more than some other areas in North Yorkshire.
“We look on a daily basis at the data in each district in order to deal with outbreaks in a range of settings as they occur. All partners are ready to act swiftly as the need occurs as is the case currently in Selby.”