The Tractor Boys began the new Championship season with a 1-0 win over the Blues at Portman Road, Joe Garner scoring on his competitive debut for his new club.
However, 18-year-old Dozzell was stretchered from the field shortly before half time after going over on his ankle in the penalty area.
"The worry is that it's a cruciate but that will be confirmed one way or another when he sees the specialist on Monday," McCarthy told the official Ipswich website.
"In terms of result and performance it was the perfect day but obviously Dozzer's injury has put a cloud over it."
Dozzell, who came through the ranks at Ipswich, has been capped by England up to Under-19 level.