"Aaron Ramsey sustained fractures to the tibia and fibula in his right leg. Yesterday evening he underwent surgery," the club said in a statement on their website.
"The operation successfully reduced the fractures and whilst it is too soon to state an exact timescale for recovery, Aaron will certainly miss the remainder of this season.
"Our thoughts are with Aaron at this time and everyone at the club wishes him all the best in making as speedy a return to action as possible."
Ramsey, 19, was treated for several minutes and had an oxygen mask on his face before he was taken straight into a pitchside ambulance in Saturday's 3-1 victory.
The injury came after a challenge by Ryan Shawcross, who later issued a statement on the club's website saying: "There was absolutely no malice in the challenge. I would never, ever go out to hurt a fellow professional.
"I am deeply upset that Aaron has suffered such a bad injury and my thoughts are with him. I would like to send him my best wishes too for a speedy recovery."
Shawcross was later called up by England for the first time when manager Fabio Capello announced his squad for Wednesday's friendly against Egypt at Wembley.
