Wilshere, who has not yet featured for the Gunners in the new Premier League season, reacted angrily to a tackle from City midfielder Matthew Smith.
The England midfielder, 25, pushed Smith to the floor and then grappled with City's Tyreke Wilson.
Players from both sides became involved before Wilshere and Wilson saw red.
Wilshere, who spent last season on loan at Bournemouth, is fit again after fracturing his lower left leg during the Cherries' 4-0 defeat at Tottenham in April.
Having set up one of Arsenal's goals, he was sent off with the Gunners leading 4-1. They won 4-3.
Arsenal manager Arsene Wenger has said he "planned" for Wilshere to stay at the club this season, despite him being linked with another loan move.
Arsenal's Jack Wilshere was sent off after grabbing an opponent around the neck in a mass brawl during an under-23s match against Manchester City.