Bailly, who has won 41 caps for the Elephants since making his debut in 2015, is one of 28 players selected by Patrice Beaumelle.
The Premier League is well-represented, with ex-Red Wilfried Zaha and Arsenal winger Nicolas Pepe also on the list, but there is no place for Bailly's United team-mate Amad.
Ivory Coast have been drawn in Group E of the tournament in Cameroon, which was originally due to be played last summer before being moved because of the COVID-19 pandemic.
The Elephants begin their campaign by facing Equatorial Guinea on 12 January, before matches with Sierra Leone and reigning champions Algeria.