The German has selected 27 players in the provisional squad for the tournament, which starts in Equatorial Guinea on January 17.
Finke has elected to omit the majority of the players who featured in Cameroon's dreadful campaign in Brazil.
Cameroon were eliminated in the group stages, having failed to win a game and scored just one goal.
Instead Finke has turned to a younger crop of players in what will be Cameroon's first major tournament since the retirement of Samuel Eto'o from international football.
Porto striker Vincent Aboubakar is likely to lead the line after netting four goals in qualification, while 21-year-old Lyon forward Clinton N'Jie - scorer of three goals in qualifying - has also been selected.
But there is no place for on-loan West Ham midfielder Alex Song, who has not featured for his country since being sent off for elbowing Mario Mandzukic in a 4-0 World Cup defeat to Croatia.
Cameroon have been drawn in Group D alongside the Ivory Coast, Guinea and Mali, and start their campaign versus the latter on January 20 in Malabo.
Squad in full:
Goalkeepers: Pierre Sylvain Abogo (Tonnerre Yaounde), Guy N'dy Assembe (Nancy), Fabrice Ondoa (Barcelona B)
Defenders: Cedric Djeugoue (Coton Sport), Nicolas N'Koulou (Marseille), Henri Bedimo (Lyon), Frank Bagnack (Barcelona B), Ambroise Oyongo (New York Red Bulls), Brice N'Late (Marseille)
Midfielders: Eyong Enoh (Standard Liege), Stephane Mbia (Sevilla), Raoul Loe (Osasuna), Edgar Salli (Academica), Georges Mandjeck (Kayseri Erciyesspor), Franck Kom (Etoile du Sahel), Patrick Ekeng (Cordoba)
Forwards: Eric Maxim Choupo-Moting (Schalke), Benjamin Moukandjo (Reims), Vincent Aboubakar (Porto), Leonard Kweuke (Caykur Rizespor), Clinton N'Jie (Lyon), Franck Etoundi (Zurich), Jacques Zoua Daogari (Kayseri Erciyesspor)
