The Black Stars, who are yet to play a game since November 2019, will face their West African neighbours in Antalya on October 9 - the encounter would be Akonnor's first game as Ghana coach since his appointment in February.
Ghana were also scheduled to face Equatorial Guinea three days later but the Central African country opted out on Thursday night due to the travel ban imposed by their government to curb the spread of the coronavirus pandemic.
Mensah has been rewarded with an invitation to the Black Stars for the first time in five years after his impressive performances for Besiktas in the Super Lig this season.
The former Atletico Madrid midfielder moved to Istanbul from rivals Kayserispor this summer and he has already scored a goal after two matches in the Turkish top-flight.
Strasbourg's Alexander Djiku, Azam FC's Yakubu Mohammed, MSK Zilina's Benson Anang, Amiens' Emmanuel Lomotey and 18-year-old forward Kamal Deen, who is based in Nordsjaelland, are the five new invitees in the team.
Meanwhile, the Ghana Football Association has initiated plans to organise another friendly match for the Black Stars after the Mali outing in order to prepare Akonnor’s squad for November’s Africa Cup of Nation qualifying fixtures against Sudan.
They sit at the summit of Group C, ahead of South Africa, with six points after two matches.
List in full
Goalkeepers: Richard Ofori (Maritzburg), Richard Ati Zigi (St. Gallen), Razak Abalora (Unattached)
Defenders: Benson Anang (Zilina FC), Lumor Agbenyenu (Sporting Club), Yakubu Mohammed (Azam FC), Gideon Mensah (Vitoria de Guimaraes). Alexander Djiku (Strasbourg), Joseph Aidoo (Celta de Vigo), Nicholas Opoku (Amiens), Kassim Nuhu (Hoffenheim).
Midfielders: Thomas Partey (Atletico Madrid), Emmanuel Lomotey (Amiens), Bernard Mensah (Besiktas), Baba Iddrisu (RCD Mallorca).
Attackers/Wingers: Andre Ayew (Swansea), Jordan Ayew (Crystal Palace), John Antwi (Pyramids FC), Eugene Ansah (Hapoel Shmona), Jefferey Schlupp (Crystal Palace), Samuel Owusu (Al Fayha FC), Kamal Deen (Nordsjaelland SC), Mohammed Kudus (Ajax SC).