MSG Media announced the move shortly after 8 p.m., urging sports fans to switch carriers.
"We certainly hope Time Warner Cable returns to the negotiating table and reconsiders our good faith proposals," MSG Media president Michael Bair said.
Time Warner says MSG is asking for a 53 percent fee hike, which would make it the most expensive sports network in the country.
Just after midnight Time Warner began broadcasting a scrolling message saying MSG had blacked out its cable customers.
"The decision to remove their programming from our lineup rests entirely with MSG," Time Warner spokesman Alex Dudley said in a statement. "MSG has again shown that they are more interested in holding New York sports fans hostage than in negotiating a deal. Rather than engage in a war of words, they should come back to the table and get a deal done."
Bair insists the network is only asking for "fair and reasonable rates that are consistent with what other providers pay for our programming."
Dudley said the company is willing to pay a 6.5 percent fee increase through the end of the NBA and NHL seasons, as the network originally requested. That deal, he said, was later pulled from the table by MSG.
The dispute does not affect Long Island residents. Time Warner serves more than 2.8 million customers in Manhattan, Queens, Staten Island, Brooklyn, Mount Vernon and the Hudson Valley, and Bergen and Hudson counties in New Jersey.
The Madison Square Garden Co., a former unit of Cablevision Systems Corp., was spun off in early 2010. Cablevision, which owns Newsday, no longer owns any shares of MSG. The family of Charles F. Dolan, Cablevision's chairman and an MSG director, controls both companies, according to MSG's October proxy statement.