Gyan, 32, who currently plies his trade for Turkish top-flight side Kayserispor and the Black Stars all-time record scorer with 51 goals in 106 caps has been overlooked - along with Andre and Jordan Ayew.
However, Kwado Asamoah, who joined Inter ahead of the new season after six spectacular years at Juventus has earned his first call-up since 2014 - when he declared himself unavailable for selection while battling injury problems.
"We don't have a new captain," coach Appiah told Ghana Web TV. "Asamoah Gyan remains the captain of the Black Stars.
"Until we announce that we have appointed a new captain, it's unnecessary for people to speculate that we have a new captain," Appiah continued. "This captaincy issue keeps coming out and brings troubles in the team.
"We want to have our peace. Ghanaians should support the team and stop bringing up issues that do not exist."
Maritzburg United goalkeeper Richard Ofori is one of the more notable inclusion after a sterling 2017/18 season in the ABSA Premiership.
Squad in full:
Goalkeepers: Lawrence Ati (Sochaux, France), Richard Ofori (Maritzburg United, South Africa)
Defenders: Harrison Afful (Columbus Crew, USA) Daniel Opare (Royal Antwerp, Belgium) Kasim Nuhu Adams (TSG Hoffenheim, Germany) John Boye (FC Metz, France), Daniel Amartey (Leicester City, England), Andy Yiadom (Reading, England)
Midfielders: Afriyie Acquah (Empoli, Italy), Isaac Sackey (Alanyaspor, Turkey), Ebenezer Ofori (New York City FC, USA), Christian Atsu (Newcastle United, England), Edwin Gyasi (CSKA Sofia, Bulgaria) Kwadwo Asamoah (Inter Milan, Italy), Thomas Partey (Atletico Madrid)
Forwards: Raphael Dwamena (Levante UD, Spain), Majeed Waris (FC Nantes, France), William Owusu (Antwerp, Belgium)