Sage was found dead in his Hollywood apartment on Friday (July 13), having allegedly been deceased for at least three days before his body was discovered.
Schwarzenegger offered support to his Expendables co-star Sylvester in a newly-released press statement.
The Terminator star said: "My thoughts and prayers are with Sly and his family. Sly has become a great friend over the past couple decades, and I know how important his children are to him.
"I want him to know that my family and I, and his fans all over the world, support him during this difficult time."
Sage was the son of Rocky star Sylvester and Sasha Czack.
His first forays into the entertainment business were guest appearances in his grandmother Jackie Stallone's Gorgeous Ladies of Wrestling shows when he was just a child.
Sage made his acting debut in 1990's Rocky V and later appeared with his father again in Daylight.
He was 36 years old at the time of his death.