The team said Wednesday night that Anthony's sister, Michelle Anthony, died of a pre-existing medical condition Tuesday in Baltimore. She had four children.
Anthony missed the Nuggets' game in San Antonio. Denver's next game is Christmas Day at Oklahoma City.
Nuggets coach George Karl says the situation "brings us down to earth" and reminds his team that there are more important things than basketball.
Anthony has been the subject of trade rumors since he spurned the team's offer of a three-year, $65 million contract extension last summer. He's averaging 24 points and 8.3 rebounds this season.
The 26-year-old Anthony has recently been hampered by a strained right elbow, sitting out the last two days of practice leading up to Wednesday night's game against the Spurs.