McCann was hit with the ban for his part in a post-match bust-up with St Johnstone goalkeeper Zander Clark, after the two sides met at Dens Park earlier this month.
• READ MORE - Neil McCann in post-match bust-up with St Johnstone ‘keeper
The pair were charged with “excessive misconduct” by the SFA after a close confrontation following Saints’ 4-0 win at Dens on March 10, and an independent panel issued the punishments following a Hampden hearing.
St Johnstone manager Tommy Wright felt television footage of the incident had “vindicated” his club and denied claims that Clark had grabbed McCann by the neck.
McCann denied slapping the goalkeeper, claiming his hand had caught the substitute as he tried to free himself.
The pair had clashed after McCann initially remonstrated with St Johnstone kit-man Manny Fowler following his side’s Tayside derby defeat.
The former Rangers and Scotland player had vowed to represent himself at Thursday afternoon’s hearing.
A statement on the Dark Blues website read: “Dundee Football Club can confirm that we have this afternoon appealed the two-match suspension handed to Neil McCann by the Scottish FA yesterday.”
• READ MORE - Neil McCann and Zander Clark hit with two-game bans for touchline clash