The 39-year-old vacated his position as a youth coach with the Gunners to become an assistant at the Bundesliga side, who have appointed Andries Jonker as head coach.
Jonker was running Arsenal's academy and opted to take Ljungberg with him to Wolfsburg, although the former Sweden international – who played for Arsenal for nine years - may return to the Emirates Stadium.
Wenger revealed he had received a promise from Ljungberg and wished Wolfsburg's new management duo well.
"We gave him permission to go, but with a promise that he will come back if there is a possibility to come back here," Wenger said of Ljungberg.
"Overall, I think it is part of his education to become a coach, to have this kind of experience.
"Hopefully we can use that later at Arsenal. Freddie has done extremely well with the under-15s here. I was in touch with him constantly during his experience there."
Jonker and Ljungberg arrive in Germany with Wolfsburg sitting 14th in the table - two points clear of the relegation zone - after previous manager Valerien Ismael lasted four months in the role.
"Andries has been at Wolfsburg before," said Wenger. "They knew him and they took advantage of the fact they know him to attract him there.
"Wolfsburg is a good opportunity because they have the third [highest] budget in the league.
"If you look at their team, their squad, they have very good players, so he has a good opportunity there to get them out of the relegation battle and as well to prepare to be their long-term coach there."