The 19-year-old midfielder was injured in a horror tackle from Stoke midfielder Ryan Shawcross in the 3-1 Barclays Premier League victory at the Britannia Stadium.
The Wales midfielder underwent surgery but it is still to early speculate when the player might return.
Shocked: Arsenal and Stoke players can hardly look at Ramsey's leg
A club statement read: 'During yesterday's match against Stoke City, Aaron Ramsey sustained fractures to the tibia and fibula in his right leg. Yesterday evening he underwent surgery.
'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 was rushed to a local hospital after the incident in the 65th minute of the game and was expected to be transferred to London today (Sunday).
Bad break: Ramsey was given oxygen as he left the field on a stretcher
Play was held up for five minutes while Ramsey was tended to on the field and a number of players appeared visibly distressed.
Shawcross himself left the field in tears after being shown a straight red card for the challenge.
Arsenal boss Arsene Wenger vented his anger at Shawcross, branding the tackle horrendous and saying his automatic three-match ban for the red card was "just ridiculous".
Stoke counterpart Tony Pulis, while condemning the tackle, defended Shawcross' character by saying he 'would never, ever go out to hurt a fellow professional'.
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