Marseille winger Ayew failed to report to the side's training camp to have his injury assessed as requested.
With the deadline to submit their 23-man tournament squad falling on Wednesday, the Ghana Football Association had told Ayew it wanted him to attend the training camp in Abu Dhabi on Monday morning so that team doctors could look at his hamstring injury.
However, Ayew did not appear and now Appiah has taken the decision to omit the 23-year-old - who made the five-man shortlist for the 2012 African Player of the Year - from his squad.
In a statement on www.ghanafa.org, Appiah said: "I have decided to exclude midfielder Andre Ayew from the Ghana squad for the 2013 African Cup of Nations.
"Following Andre's inability to join the Black Stars squad by Monday morning for Ghana's team doctors to assess the extent of his injury and fitness for the tournament, I have decided to work only with the players currently in camp.
"As Andre plans to arrive on Tuesday it means he would be unable to join any of my six training sessions before the Confederation of African Football's Wednesday deadline for the submission of the final squad."
Ghana won the last of their four African Nations Cup titles in 1982 but in the last three editions have finished third, second and fourth respectively.