Gunning had been offered the ban after the SFA compliance officer reviewed footage from United's 1-0 reverse to Celtic last weekend.
The player decided on a personal hearing in Glasgow today, and the original decision has been upheld.
Gunning's punishment comes for kicking Celtic defender Virgil Van Dijk off the ball during the Tannadice encounter.
A statement from the SFA read: "Compliance Officer Reference upheld and a three-match suspension applied."
Gunning was playing for just the second time this season on Saturday following an earlier sending-off against Hibernian.