Over the international break, it was revealed that the 27-year-old had gone under the knife to treat an issue that had been plaguing him for some time, and the initial expectation was that he would be around for about eight weeks.
That timeline would have put White on track for a return in the middle of January, but speaking in Friday's pre-Nottingham Forest press conference, Arteta suggested that he will be sidelined for longer than first envisaged.
"Ben is going to be out for months. It's been different kind of struggles, it's never been the same thing, but we had to make a decision in the last few weeks, unfortunately," the Gunners boss told reporters.
"We know that Ben is going to push every boundary but it got to a point where we had to protect the player and we decided to do the surgery. He agreed with that, and obviously it will keep him out for a few months. We have to see how he reacts post-surgery, I don't expect him to be out for half a season or year but I cannot tell you exactly [how long]."
White out for "months" as Takehiro Tomiyasu struggles continue
White joins Takehiro Tomiyasu (knee) and Kieran Tierney (hamstring) in the Arsenal medical room; the latter is still not ready to make his first-team comeback despite taking part in a few full training sessions.
Regarding the injury-riddled Tomiyasu, who has only managed one appearance this season so far, Arteta revealed that the Japan international would be spending a few weeks away from North London in the hope of 'unlocking' a solution.
"He's going to be away now for a few weeks for him to continue with his training and to change his environment a little bit because it's been really tough for him as you can imagine," Arteta said on Tomiyasu.
"He's one of the guys where the only thing he wants to do is to work 24 hours to get better and he feels terrible when he's not fit, so it's a real shame. We're going to give him the best opportunity to try and unlock something to help him to have him back as quickly as possible, but I think we need to be patient."
However, the Arsenal boss was able to share positive updates on a few other injury doubts, including Bukayo Saka and Declan Rice, both of whom pulled out of the England squad for November's UEFA Nations League matches with Greece and the Republic of Ireland.
Saka, Rice on track to be fit for Forest
"They have had their first partial session today, so very good as well," Arteta said, before also going on to deliver good news on Belgian attacker Leandro Trossard and Italian defender Riccardo Calafiori.
The latter is on course to make his comeback a few weeks after sustaining a knee injury in the Champions League, while the issue that Trossard suffered on international duty does not appear to be too severe.
"Ricci trained today, so his rehab is going really well. He was able to do certain things last week with the physios, and trained on the pitch this week with us and today, so he will be in the squad," Arteta concluded.
"Trossard seems to be OK, he trained this morning and seems to be feeling good. We will assess everything with the doctor right now, as he was able to be part of that session, so that's good."
Arsenal start the weekend in fourth place in the Premier League table, only above Nottingham Forest on goal difference, and Arteta has been warned that Saturday's match is his "biggest game of the season" so far.