RWJBarnabas Health, which boasts 11 acute-care hospitals across the Garden State, announced the news in a statement on Wednesday.
Back in May, the private company mandated that all staff at a 'supervisory or above level' be fully vaccinated by June 30.
In Wednesday's statement - which was first obtained by ABC News - RWJBarnabas Health stated that a 'vast majority' of staff complied with that order.
'As of July 14, 2,979 staff members, or 99.7 percent, who are at the supervisor level and above, have been fully vaccinated or received medical and religious exemptions or a deferral,' the company said.
'Regrettably, six staff at the supervisor level and above have not complied with the mandate and are no longer employees of RWJBH, per our policy.'
The identities of the six workers were not disclosed.
RWJBarnabas Health is New Jersey's largest private employer, with more than 35,000 staffers, many of whom do not work directly with sick patients.
But the company now says it has plans to require all hospital staff to be vaccinated. It will announce a vaccine deadline date for those employees 'in the coming days.'
Meanwhile, other private New Jersey hospital systems are not enforcing the same rules.
Atlantic Health System, which serves 11 New Jersey counties, told NJ.com that it is 'giving workers the option whether to vaccinate'. The company said most have chosen to do so.