General Manager Chris Grant revealed in a statement Varejao had been admitted to the Cleveland Clinic, where he was undergoing treatment.
Afterwards, the nine-year veteran will be placed on blood-thinning drugs for about three months.
One of the NBA's top rebounders, Varejao is expected to make a full recovery.
"Clearly our players' health is our top concern and we are disappointed for Anderson and his family," Grant said. "We know what a competitor he is and how much he wants to be on the court helping his teammates."
The 6-foot-11 Brazilian had already been sidelined after undergoing surgery for a small muscle tear in his right leg.
Varejao was leading the NBA with 14.4 rebounds per game and was scoring 14.1 points per contest at the time of his Dec. 19 injury.