Aguirre, 51, was rushed to The Medical Center of Plano and the family confirmed that he is "in stable condition and is expected to make a full recovery."
"Mark suffered a fall while working out today at a local gym," Aguirre's family said in a statement released later Wednesday. "He has been admitted to The Medical Center of Plano and is not being treated for a heart attack. He is listed in stable condition and is expected to make a full recovery. The Aguirre family would like to thank all those who have expressed their concern about Mark's condition. In order to expedite Mark's recovery, the family respectfully asks that their request for privacy be honored."
Former Mavericks general manager Frank Zaccanelli told ESPN.com's Marc Stein that Aguirre was "being held [at the hospital] for observation and a few more tests, but he's expected to have an absolute full recovery."
Zaccanelli also told ESPN 103.3's Galloway & Co. that Aguirre suffered what he called a clogged vessel.
Aguirre played 7½ seasons with the Mavericks in the 1980s and still holds the team single-season scoring record in the 1983-84 season. He helped lead the franchise to its first Western Conference finals in 1988. He later won two championships with the Detroit Pistons.
Aguirre took DePaul University to the Final Four in 1979 as a freshman. When the Blue Demons had a coaching vacancy last year, he expressed interest in the job.
He has also been an assistant coach with the Knicks and Pacers.
Jeff Caplan covers the Mavericks for ESPNDallas.com. Information from ESPN.com's Marc Stein contributed to this report.