The teenage midfielder, who skippered the U's in their 3-0 defeat at the hands of Town at the Weston Homes Community Stadium, was forced off at half-time after suffering the injury in the opening stages of the match.
Striker Dan Holman was also withdrawn at half-time because of injury and both players are doubtful for Colchester's friendly matches against Dover Athletic (tomorrow night) and Dagenham and Redbridge (Saturday).
U's boss Dunne said: “Alex has got a pretty bad gash on his shin that needing stitching and we didn’t want to take any risks.
“It was a shame, because Alex and Dan were very good and the changes we had to make at half-time kind of upset us a bit."
Meanwhile, Dunne said he was pleased with the contribution of youngster Dion Sembie-Ferris, who made his maiden senior appearance for Colchester after coming on with 20 minutes to go against Ipswich.
The young winger joined the U's academy last year from St Neots Town.
Dunne added: “Dion was brought in based on the fact that Tosin Olufemi played 90 minutes against Southend.
“I didn’t want to give Tosin any extra game time against Ipswich because of the injury risk.
“Dion did really well when he came on, as I thought did all of the players."
For all of the latest Colchester United news, see the Daily Gazette.