The 24-year-old made his return against Newcastle Under-21s earlier this month after breaking his fibula in August.
Before Monday, his last goals were for his country as Roy Hodgson's side beat Slovenia 3-2 in June.
Wilshere featured in five of England's first six qualifying fixtures for this summer's European Championship.
Arsenal and England midfielder Jack Wilshere scored his first goal for 10 months as the Gunners' Under-21 team lost 2-1 to West Brom on Monday.