The Jiangsu Suning striker has asked to be excused from the games due to an injury picked up during last week's Chinese league clash with Shanghai SIPG.
Although he lasted for the entire duration of the match, an ankle injury during the fixture has taken a toll on him, sources said.
The Black Stars face World Cup-bound Japan on May 30 before facing Iceland on June 7.
Boakye's latest injury is a setback to his ambitions of cementing a starting place in the Black Stars on the back of recent good performances.
The striker, who netted on his debut against China in 2012, scored twice as the four-time African champions beat Congo 5-1 in a World Cup qualifier in October.
He was out of the team for a while before the fateful game, but after registering the double, he has been a regular feature in Appiah's squad lists.