The seventh seed, a Melbourne quarter-finalist in 2022, won the opening set 6-3 against Nuno Borges of Portugal but then lost the next two 6-4, 6-4 before retiring.
It was not immediately clear what the injury was, but the 25-year-old walked gingerly to the net to shake hands with his opponent.
The 25-year-old, who had appeared bothered by his left leg, walked gingerly to the net to shake hands with his opponent and said afterwards that cramp was to blame.
The problem began at the start of the third set, he said.
"I can't recall (cramping) ever in my life this early in a tournament, this early in a match," he said.
He was not sure if temperatures close to 30C were to blame, but said it was impossible to continue.
"I don't like to be on the court that way. I want to be on the court winning," said Auger-Aliassime, who has won eight ATP titles.
"I want to be on the court competing with my opponent. I don't want to be just standing there like a punching bag."
"It is part of tennis and it's a long schedule and physically it's demanding, so I can understand," the 46th-ranked Borges said in his on-court interview.
"I hope he gets better quick and back to his best level.
"It's a great win for me either way, really happy to push through this one and get another opportunity on Wednesday."
Borges faces Australian wildcard Jordan Thompson or Juan Manuel Cerundolo of Argentina next.