A total of 55 new cases were confirmed between Tuesday and Thursday alone, according to the New York Daily News.
The federal prison had seen just 25 cases since March but as of Tuesday had a total of 80, said the Bureau of Prisons.
In addition to inmates, 49 members of staff have also tested positive, stated the Daily News.
Ms Maxwell has been housed in the facility since her arrest in July while she awaits trial on four counts of sexual trafficking of a minor and two counts of perjury.
Her lawyers are expected to renew her request to be released on bail and they had requested a private meeting with prosecutors before US District Judge Alison J Nathan.
The judge turned down that request for a private hearing and asked both sides to organise a schedule for her bail request, according to the Miami Herald.
Ms Maxwell was placed in quarantine on 18 November after being exposed to someone who had tested positive for Covid.
It is not known if she also had Covid.
Her lawyers originally argued that she should get bail because of virus fears and had proposed she stay in a New York hotel until her trial in July.
She was denied bail due to her access to funds and because she holds a French passport and France does not extradite its citizens to the US.