NEW YORK (Reuters) - Serena Williams has pulled out of the U.S. Open because she is still recovering from surgery on her right foot, the American world number one said on Friday.

Williams, who won her 13th grand slam at Wimbledon earlier this year, cut her foot on broken glass at a restaurant in July and has not played since.

"It is with much frustration and deep sadness that I am having to pull out of the U.S. Open," Williams said on the tournament's website (http://www.usopen.org/). "My doctors have advised against my playing so that my foot can heal."

With Belgian Justine Henin announcing on Wednesday she would not be fit to play in the U.S. Open and defending champion Kim Clijsters losing in Montreal after an injury scare, the year's final grand slam is shaping up as a wide open affair.

"There are still so many other big names out there who can do well," said Clijsters, who promised to be in Flushing Meadows to defend her crown despite a nagging hip injury that will require an MRI next week. "Serena and Justine are two big names but there are plenty more out there.

"I don't look at the draw in that kind of way, I just focus on my matches and obviously now I am trying to be in the best shape possible to compete."

A fan favorite and television ratings grabber, Williams is sure to be missed especially after her explosive and controversial exit from last year's event.

Called for a foot fault in her semi-final against Clijsters, Williams exploded in an ugly outburst threatening a line judge during a confrontation that ultimately cost her the match.

"It doesn't change much," said Russian Vera Zvonareva, who lost to Williams in the Wimbledon final in early July.

"Serena is a great player and is great to watch but there are so many great players.

"It's still going to be very tough for everyone."

(Reporting by Steve Keating in Montreal and Simon Evans in Mason, Ohio; Editing by Frank Pingue/Greg Stutchbury)