The 30-year-old Brazilian, who was the NBA's top rebounder until a knee injury requiring surgery sidelined him in December, was admitted to the Cleveland Clinic last Thursday where he is being treated with blood thinners.
He will need to remain on blood thinning medication for approximately three months but is expected to make a full recovery, according to the Cavaliers.
"Clearly our players' health is our top concern and we are disappointed for Anderson, and his family," Cavaliers General Manager Chris Grant said in a statement.
"We know what a competitor he is and how much he wants to be on the court helping his team-mates. In the meantime, he has our full support and we look forward to welcoming him back as he recovers."
Taken in the second round of the 2004 NBA Draft, Varejao was traded to the Cavaliers that same year and has spent his entire career in Cleveland.
Varejao, who has not played since suffering his knee injury, was averaging a career-high 14.1 points and a team-leading 14.4 rebounds in 25 games for a Cavaliers team that is 14th in the 15-team Eastern Conference with 40 games left in the season.
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