The Republic of Ireland ace was offered the ban by the SFA on Tuesday for allegedly kicking Hearts forward Callum Paterson in last Saturday's 0-0 draw at Fir Park.
The Steelmen have responded to the notice of complaint, issued by SFA compliance officer Vincent Lunny.
A statement from the Fir Park club read: "Motherwell FC have notified the Scottish FA of the club's intent to contest the fixed two-match suspension offered to Darren Randolph by the compliance officer.
"The matter will now be referred to the judicial panel with a fast track tribunal convened today. The club will make no further public comment on the matter until that process is complete."
If the appeal is unsuccessful, Randolph will miss Saturday's William Hill Scottish Cup tie at Aberdeen and the visit of Ross County for an SPL clash on Saturday week.