Bosh sat out the All-Star Game and 3-point contest this past weekend because of what the team called a strained calf.
The Heat issued a statement midway through Wednesday's practice saying that Bosh would not be at the workout and would not travel with the team for Friday's game against the Hawks.
They did not offer specific details on Bosh's condition or whether he might return this season.
Bosh is expected to make a statement updating his condition in the coming days.
Heat players and coaches have been in contact with Bosh in recent days. Guard Dwyane Wade suggested Wednesday that Bosh's condition appeared far less serious than the one that ended his season after last year's All-Star break, when blood clots traveled to his lungs.
"It's not a health scare like it was last year at all," Wade said after Wednesday's practice. "None of us are overdoing it from that standpoint. So he's fine. I'm not going to speculate anything. None of us are doctors. He's in great spirits. He has a positive outlook on things. He's showing us he's in good spirits."
Added former Heat teammate LeBron James: "Guy means so much to not only the Heat family but his personal family as well. Just a great guy, a professional, a great guy and for something like this to happen to him after he was cleared, it just sucks. It sucks big time. His health is the No. 1 care and obviously basketball comes secondary to what he's going through right now. It's just tough."
Bosh, 31, missed the final 30 games of last season when it was discovered that a blood clot had traveled to his lungs, which led to an eight-day stay in a Miami hospital followed by months of rehabilitation.
Bosh is having his most productive season in six years with the Heat. He leads the team in scoring at 19.1 points per game and in 3-pointers with 81.
Miami coach Erik Spoelstra said Bosh's absence is the latest test to the team's resilience. Miami has already endured two trades and two disciplinary suspensions, and assistant coach Keith Smart has twice needed to step aside in recent months to receive treatment for a rare form of skin cancer.
"These kinds of things also show you how fragile things are in life and in this business," Spoelstra said. "That's why the journey and the friendships and the relationships and building toward something together -- going through all of it -- those are experiences that help you grow. And they help you get closer together as a group. It immediately pulls you right into perspective."
The Heat (29-24) sit in fifth place in the Eastern Conference entering Friday's game in Atlanta.
After Bosh left the lineup last season, the Heat finished 37-45 and missed the playoffs for the first time in six years. His comeback from blood clots made him one of the NBA's most compelling stories through the first half of this season.
"I was just trying to make it through," Bosh told ESPN.com last week of overcoming last season's health scare. "But just overall, it was about being smarter with my health. It was just about spending more time with my family, appreciating different things and seeing different things that I hadn't necessarily seen before. That's probably the most important thing."
Information from ESPN.com's Dave McMenamin was used in this report.