Abeid sustained a broken toe while on duty for the north Africans after being selected for their qualifying matches with Ethiopia and Malawi in November.
Depsite the blow, Abeid was selected in Christian Gourcuff's squad for the AFCON tournament in Equatorial Guinea, which starts on January 17.
However, the Newcastle United midfielder has now been replaced by the uncapped Ahmed Kashi of Metz - who had been on the standby list for the competition.
Meanwhile, defender Belkalem - on loan at Trabzonspor - has been deemed unfit to participate by the team's doctors due to a hamstring injury sustained while playing for the Turkish Super Lig side.
Algeria are looking to win the AFCON for a second time having previously claimed the title in 1990. However, they have been drawn in a difficult group alongside fellow former winners Ghana and South Africa and 2002 finalists Senegal.
Gourcuff's men play their first Group C match against South Africa in Mongomo on January 19.
