Sources close to the situation said Alston, who did not attend the game, is considering retirement.
The Heat initially announced that Alston missed the Atlanta game for "personal reasons." But later revealed Alston has not made himself available to the team by anything other than text message since losing his starting spot at point guard before Thursday's overtime win over the Los Angeles Lakers.
"Rafer Alston, while having made contact with the team via text message, has made himself otherwise unavailable to the team. As a result he has been suspended indefinitely," the team said in a release.
Alston could not be reached for comment. He did not immediately respond to an e-mail message.
Alston began his second stint with the Heat in January after securing a buyout from the New Jersey Nets.
The 33-year-old was benched for the final three quarters of Tuesday's victory over Golden State and did not play against the Lakers. Alston started at point guard in his first 25 games back with Miami before being replaced Thursday by Carlos Arroyo.
Alston is in his 11th NBA season and as recently as last season helped Orlando weather the injury loss of Jameer Nelson to reach the NBA Finals after the Magic acquired him in a deadline-day trade with Houston.
He is averaging 6.6 points and 2.9 assists.
The Associated Press and ESPN Senior writer Marc Stein contributed to this report.