The winger pulled up with a hamstring injury in the 23rd minute of the 5-1 win at Crystal Palace last weekend.
Saka was pictured leaving Selhurst Park on crutches after the game.
Arteta then confirmed after the Gunners' 1-0 win over Ipswich that Saka has undergone surgery on his injury.
"He has had a procedure and everything went well, but unfortunately he will be out for many, many weeks," the Arsenal manager said.
Going into more detail on his expected spell on the sidelines, he continued: "It will be more than two months. I don't know exactly how much longer.
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"It will depend on how the scar tissue starts to heal, the first week or so, and the mobility of that. It is very difficult to say."
Arteta added: "The replacement of Bukayo is going to be the team.
"There were moments where it flowed well tonight and moments where you could see there is still work to do. But I am certain that we are going to do that.
"We have to rely on the team and not the individual."
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It means Saka will play no part in the Premier League, FA Cup, Carabao Cup or the Champions League until March at the earliest.
Arteta had previously claimed that Saka would be 'out for many weeks' and that his hamstring injury was 'not looking good.'
Saka had previously picked up a hamstring injury on international duty in October during England's defeat to Greece.
He then appeared to tweak it again during his club's 1-1 draw with Chelsea in November.
Between now and the end of January, Arsenal will have played ten games, which includes league showdowns with Tottenham, Aston Villa and Brighton.
Meanwhile, their first match of February sees them take on reigning Premier League champions Manchester City.
Also in that run are two Champions League group stage games, Arsenal's FA Cup clash at home to Manchester United as well as the first leg of their Carabao Cup semi-final tie against Newcastle.
He's also set to miss the second leg against the Magpies as well as Premier League showdowns against Leicester, West Ham and Nottingham Forest.
Bukayo Saka spotted on crutches after Arsenal's win over Crystal Palace
Saka has started all but two of Arsenal's 18 Premier League matches so far this season.
The Three Lions forward has also started in five of the club's Champions League fixtures, along with one Carabao Cup fixture.
Once again, Saka has been Arsenal's standout player this term.
He has already chipped in with nine goals and 13 assists in all competitions - just 12 goal involvements off his tally from last season.
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Saka would have been hoping to add to his tally at Selhurst Park on what was his 250th appearance for Arsenal.
Only Cesc Fabregas and David O'Leary have hit the landmark milestone at a younger age than Saka.