The England international was sidelined at the back end of the 2014/15 campaign by an injury that initially was only expected to keep him out of action briefly. However, the forward went on to miss the last six matches of the Gunners' campaign, including the FA Cup victory over Aston Villa, and is not yet fit to play.
Welbeck is joined on the sidelines by midfielder Tomas Rosicky who is also struggling with a knee injury.
Other absentees from the 27-man touring party for the Barclays Asia Trophy are Carl Jenkinson, Joel Campbell, Serge Gnabry and Yaya Sanogo who are expected to either be loaned out or sold in the coming weeks.
After doing duty for Chile and Colombia respectively at the recent Copa America, Alexis Sánchez and David Ospina are given an extended break and have not yet reported for training.
Academy players Daniel Crowley, Chris Willock, Alex Iwobi and Jeff Reine-Adelaide have been included in the squad.
Arsenal play a Singapore Select XI next Wednesday and either Stoke City or Everton three days later.