All three individuals are asymptomatic and have entered quarantine.
The Madison Square Garden Training Center will undergo a "thorough cleaning" before the franchise reopens it.
New York is not disclosing the names of the employees who contracted the virus.
The outbreak comes as teams are preparing for training camps to open in advance of the league's December 22 start.
Unlike the end of last season, the NBA does not plan to place all teams inside a bubble and will instead work to keep teams on as normal a schedule as possible. Tuesday's news doesn't signal a delay to the Knicks' season, but it could give other clubs around the league reason to pause and review protocols before practices begin.
There is no timeline for the Knicks to reopen their facility.