The Republic of Ireland international was on Tuesday offered the punishment by the SFA for allegedly kicking Hearts forward Callum Paterson in Saturday's 0-0 SPL draw at Fir Park.
Randolph's case was given a fast-track tribunal after Motherwell responded to the notice of complaint ahead of Wednesday's deadline.
Motherwell said on their official website: "Following a fast track tribunal with the judicial panel this morning (Thursday), Darren Randolph's suspension has been upheld and he will now miss the next two matches.
"The hearing, which lasted for almost 90 minutes, heard contributions from the player himself, alongside goalkeeping coach Gordon Marshall.
"However, the three-person panel upheld the initial offer of a suspension and the Republic of Ireland international will now miss games against Aberdeen (Scottish Cup) and Ross County (SPL)."