Annan, who recovered from a groin injury during pre-tournament training in South Africa, sustained the fresh injury on Sunday.
Medical tests reveal the Norway-based player need more days to fully recover from pain in his thigh.
His absence is a big blow for the Black Stars and the 23-year-old, who has been struggling with a knee injury.
"I think he was forcing too hard to impress the coach after recovering and that caused the problem," a source in the Black Stars camp told Ghanasoccernet.com at the tournament in Angola.
"We will miss him but we have an adequate replacement for him."
Annan should be available for Ghana's last Group match against Burkina Faso in Luanda on 19 January.
Meanwhile, defender Hans Adu-Sarpei has recovered from his injury and been training with the team.