Team spokesman Tim Donovan said the man, who was not identified, was OK and that team trainers tended to him in the air for what was believed to be a diabetic coma.
"He had like passed ou, but they brought him back. And then, we made an emergency landing in Chicago. The paramedics and everybody came and got him and took care of him," Heat forward Quentin Richardson said.
When the plane landed in Chicago, the man was taken to a hospital. He was reportedly OK Sunday evening.
The flight eventually resumed, and the Heat landed in Miami at 5:04 a.m. Sunday.
"Just landed back in the MIA feels good to be back home safe and sound," Heat guard Daequan Cook wrote on his Twitter feed.
Heat guard Dwyane Wade wrote on Twitter about the surprise landing.
"Hey everyone pray for our pilot," Wade wrote. "... He went into a Coma. God bless this man and his family."
Donovan said the man was in the cockpit when he became ill.
The team was returning to Miami after beating the Minnesota Timberwolves 97-84 Saturday night.
(The Associated Press contributed to this report.)