The Gunners will take a 27-man squad to the Far East in the first leg of their pre-season preparations, with summer signing Petr Cech joining up with his new team-mates for the first time since a Â£10million switch from Chelsea.
Welbeck, though, is to remain in London as he looks to shake off the knee problem which kept him out of the final few weeks of the season, missing both the FA Cup final win over Aston Villa and England's June internationals
Wenger sai d on the club's official website, www.arsenal.com: "Welbeck isn't completely recovered from the problem he had
He is not back in full training, so he will stay behind."
Speaking last month, Welbeck indicated there was no serious issue, just needing more time to recover
He said: ''It was worse than we first thought it was, but it is just a natural healing period and usually I heal faster than others."
Czech midfielder Tomas Rosicky, who along with captain Mikel Arteta has signed a contract extension, is also not part of the squad for Singapore because of what Wenger describes as a small injury picked up on international duty
Goalkeeper David Ospina, linked with a move away from the club following Cech's arrival, has been given extra holiday following the Copa America, as has key man Alexis Sanchez, whose penalty in the shoot-out won the final for hosts Chile
While the likes of Calum Chambers, who has cut short his time off after the European Under-21s Championships, Chuba Akpom and 18-year-old American Gedion Zelalem will all hope to get some game time on the Asia tour, Carl Jenkinson, Yaya Sanogo and Joel Campbell were not included in the group and appear likely to be sent out on loan for next season
Arsenal play a Singapore XI on July 15, then are scheduled to face either Everton or Stoke
The Gunners return to England to host the Emirates Cup on July 25/26 ahead of the FA Community Shield against Chelsea at Wembley on August 2 and will open the new Barclays Premier League campaign with a televised home game against West Ham on Sunday, August 9
Source : PA