Quinn stated her position in a letter released Wednesday. A City Council subcommittee held a public hearing on the issue on the same day.
The garden had requested to operate at the site in perpetuity. Last month, the city planning commission approved a 15-year extension.
In her letter to the garden's president and CEO Hank Ratner, Quinn said finding a new home for the arena is the only way to address the development of a new Penn Station and its surrounding area.
She called for a commission that would find the garden a new location in Manhattan.
A representative for the Garden declined comment.
