Colchester United have promised action after two fans ran on the pitch during Tuesday's home loss to Forest Green.
The incident happened late in the League Two game, which they lost 3-0.
Aston Villa captain Jack Grealish, Manchester United's Chris Smalling and Rangers' James Tavernier were accosted by pitch invaders at the weekend.
A Colchester statement read: "We will conduct a thorough investigation into the incident and look to take the most stringent action possible."
The statement continued: "We will also co-operate fully with the football authorities should they wish to conduct their own investigation into this incident."