Ramsey was one of the stand-out players at Euro 2016 and was named in the team of the tournament as Wales reached the semi-finals in France.
However, Wenger’s eagerness to take advantage of the 25-year-old’s stunning form for his country backfired as Ramsey limped off with a hamstring injury in the opening day defeat to Liverpool.
“Ramsey will not be available,” said Wenger.
“I’m disappointed because he has worked very hard and he had a few little setbacks that forced us to be cautious with him.
“He’s on the last stage, he’s building up his fitness. Next week will come too early.
“We have decided that we will give him a complete pre-season now, even if he misses more games.”
Wenger also confirmed that Olivier Giroud is still out and will not be available for Saturday’s game with Swansea at the Emirates.
However, there was good news as Francis Coquelin and Lucas Perez returned to full training over the international break, while Carl Jenkinson is ready for a return after nine months out with a cruciate ligament injury.
“Coquelin is back,” Wenger added. “Apparently we have good news [from international players].
“He [Jenkinson] will be back tonight playing with the Under-23s. He is available to compete for places.”
Arsenal have to deal with the visit of Swansea this weekend with new manager Bob Bradley taking charge for the first time since replacing Francesco Guidolin nearly two weeks ago.
The Gunners have struggled against the Swans in recent season, only managing one win in their last five games between the sides, and Wenger has told his side to show they can handle the tag of being favourites.
“Last year we had a very negative experience with Swansea that killed our chance to win the championship,” Wenger said.
“We have to re-focus because all the players have been away. We have to show we can deal with being favourites, we didn’t always do it last season.
“If I look at the results after international break it is not negative. It’s not only that. We play in a very difficult Premier League.
“There is room for improvement.”Reuse content