The decision has been met by criticism, but Southgate has said that the 26-year-old, who has scored twice in 34 England appearances, was "not as effective towards the end of the season".
"Jack had good spell in the lead up to Christmas and just after, not as effective towards the end of the season. We think other guys deserve their place in the squad," Southgate told reporters. "Jack has of course been in our thoughts. We selected him in March but he hasn't played a game for us.
"We've been pleased with the players who played in November and March. The only midfielder we added is Fabian Delph who had a fantastic season with the champions."
Wilshere scored twice and registered six assists in 38 appearances for Arsenal during the 2017-18 campaign.