The England striker was forced off in the first half of the 2-2 draw with Man City and faces a long spell out
The Arsenal striker underwent scans on his right knee after he limped out of the Gunners' 2-2 draw with Manchester City at the weekend.
And the scans revealed "significant cartilage damage" which has ended Welbeck’s hopes of representing England at Euro 2016.
An Arsenal statement revealed the former Man United man has already had surgery on the knee.
"Specialists determined surgery was required after scans and tests revealed significant cartilage damage," it read.
"Danny will miss the Euro 2016 Championship in the summer and his full recovery is expected to take approximately nine months.
"Everyone at Arsenal will be working hard with Danny throughout his recovery and look forward to seeing him back on the pitch as soon as possible."
Welbeck tweeted: "I will be back stronger!"
After the game Arsene Wenger revealed Welbeck was "very down", suggesting the forward knew he was facing a lengthy lay-off.