The Cavs have a 34-30 record but have lost nine of their last 12 games. They are fifth in the Eastern Conference playoff standings.
The 61-year-old Silas, who previously coached New Orleans and San Diego, became Cleveland coach June 2, 2003. His overall record with the Cavs was 69-77.
"I believe we needed to make this change to put the Cavaliers in the best position to make the playoffs and make the improvement we believe is possible," owner Dan Gilbert said.
Malone joined the Cavaliers in September. Last season he was an assistant with the New York Knicks and before that with the Indiana Pacers.
"We have confidence in Brendan Malone and will support him completely," General Manager Jim Paxson said "Brendan is an NBA veteran coach that has coached on championship teams and knows what needs to be done moving forward."