The veteran forward and the Blueshirts had reportedly agreed to terms on a one-year contract worth approximately $1.6 million on Saturday.
Arnott traveled to New York to meet with doctors to undergo a physical this weekend. It was revealed later on Sunday that Arnott did not pass the test.
Although the reasons relating to his failing the physical have yet to be made public, Arnott did undergo knee surgery this past summer.
In 72 games with the St. Louis Blues last season, Arnott collected 17 goals and 17 assists for 34 points.
Arnott is now one again an unrestricted free agent.