The former Arsenal player has been an unused substitute for the last two games, but has had to admit defeat in his efforts to play through the pain barrier.
Benitez said: “Today we have had the operation of Hayden for his ankle that had some problems. He needed an operation and it is being done now.
“It seems that it is not very, very serious, but it could be four weeks more or less. It depends how it goes.”
There was better news for the Sky Bet Championship leaders, who face Aston Villa at St James’ Park on Monday night, as utility man Vurnon Anita returned to training after his own ankle problem following more than a month out.