Kaleta consulted with his agent and the NHL Players’ Association following Tuesday’s suspension, according to McKenzie.
The 27-year-old agitator has already served three games for his illegal check to Jack Johnson’s head in Thursday’s 4-1 loss to Columbus.
Kaleta has been suspended four times since 2009-10 and twice in his last 21 games.
The appeal goes to NHL commissioner Gary Bettman first. Kaleta is still suspended through the appeal process.