Mustafi damaged his hamstring in the FA Cup semi-final win over Manchester City and was initially considered doubtful for next week's final against Chelsea.
Arteta confirmed the full extent of the injury after the 3-2 Premier League win against Watford, however, with the Germany international ruled out for weeks rather than days.
Asked if Mustafi will miss the start of next season, which is due to begin on 12 September, Arteta told reporters: "Yes, he will.
"It is a nasty one. He pulled the tendon of the bone of his hamstring and that's normally a lot of weeks."
Arsenal has also had to make do without fellow centre-backs Calum Chambers and Pablo Mari due to long-term injuries, with both players in a race to be fit before the end of the year.
Despite the arrival of William Saliba from Saint-Etienne, Arteta understands the need to bring in another player during the close-season.
"I already mentioned to you three central defenders that are not available and we haven't had them available for a long time anyway during this season," he said. "We will have to address that."
After concluding a disappointing Premier League campaign with three points against Watford - a result that relegated it opponent - Arsenal's focus now turns to its cup final against Chelsea.
Arteta has some big selection calls to make but has already decided Emiliano Martinez will start in goal, despite Bernd Leno's return to training this week from a month-long absence.
"Emi has earned his place with another brilliant performance again today," Arteta said. "When the team needed him he made some fantastic saves.
"Bernd is still recovering from his injuries so Emi's the one now. Let's hope that he's available for the game and if that's the case he will start the final."
Pierre-Emerick Aubameyang inspired Arsenal to its victory over Watford with two first-half strikes, either side of Kieran Tierney's first goal for the club.
Troy Deeney and Danny Welbeck pulled goals back for the visitor to set up a nervy finish, but Arteta is expecting a different type of performance against Chelsea.
"It was a crazy game right from the start," he said. "We allowed them too many balls in the box - this is where they're really dangerous.
"They had some really good quality moments with the ball in the final third but we weren't at the races without the ball like we've been doing in the last few games.
"But it will be a completely different game next week. First of all from the mental side it will be equal - how much they want it and how much we want it.
"I don't think that was the case today because of the necessity they had, the way they had to go to the game was different to ours.
"Normally you can see that when you don't have the ball. Hopefully it will be different."