The Rangers had until Tuesday to accept the figure for next season or let him go. Zherdev reportedly sought $4.5 million in arbitration after the Rangers made a $3.25 million qualifying offer.
An arbitrator awarded Zherdev $3.9 million on Sunday.
"With the additions we've been able to make this summer, we feel we've been able to add scoring and offense from the wing position," New York general manager Glen Sather said in a statement. "Following the arbitration process and subsequent award given, we feel it is in our best interest to walk away and continue to explore all available options to improve our roster."
The 24-year-old Zherdev played in all 82 games last season, his only one with the Rangers, and had 23 goals and 35 assists for 58 points -- second on the team to Nik Antropov, who came over from Toronto at the trade deadline.
New York's top three scorers from last season will not return.
Antropov left the Rangers for Atlanta last month via free agency, and Scott Gomez, who tied Zherdev with 58 points, was traded to Montreal.
Zherdev, acquired in a trade with the Columbus Blue Jackets last summer, had no points and was a minus-3 in the Rangers' seven-game, first-round playoff series loss to Washington.
In 365 NHL regular-season games with the Rangers and Columbus, Zherdev has 99 goals and 140 assists.