Some 101 people have now tested positive for the virus in the district, and the case rate has rocketed from 46.3 per 100,000 people last week to 111.5 this week according to NHS data.
On Monday night it was confirmed that the outbreak has centred on the Clipper warehouse, a short distance from Selby town centre.
A spokesperson for Clipper confirmed a number of staff had tested positive and said: "As the health and wellbeing of our staff is our number one priority, we are maintaining our social distancing protocols, conducting daily on-site testing and communicating regularly with staff and the Environmental Health Officer, who has visited the site in the last week and verified our approach.”
The company has said there is no evidence that anyone contracted coronavirus at the distribution centre.
Richard Webb, director of health and adult services at North Yorkshire County Council, said there were concerns the rate could continue to rise as extra testing across Selby was underway to manage the outbreak.
He said: "The last few days have been dominated by the Selby outbreak, showing how one outbreak can cause significant turbulence and concern.
"I think we should be prepared for a further rise in these figures because we're doing a very active targeted outbreak management programme within Selby."
Public Health England have been working with Clipper to contain the outbreak, and have not given the warehouse guidance to close down operations, it was confirmed. Test and trace of people who have tested positive is underway and community spread is being monitored.
No cases of the Indian or South African variant have been detected, with the majority of cases being the Kent variant, which has been the dominant strain in the UK for several months.
All staff at Clipper are being PCR tested each shift, and are being urged to take extra care if visiting pubs and outdoor hospitality after work.
Victoria Turner, from Public Health England, said: "Quite a few environmental health and health and safety executive officers have been on the site to review the measures in place which have generally been good."
Clipper employs over 10,000 people across 55 sites. The Selby warehouse is the returns and refunds centre for online superstore ASOS.
Cases in North Yorkshire are now at 31.7 per 100,000 people compared to the England average of 24.2.
And they are also rising in Craven, where they are at 45.6 cases per 100,000.