Kyrgios appeared to clutch his elbow in discomfort during the match with world number 58 Kovacevic, and managed to win a point with one of his trademark underarm serves in the second set.
The loss will not help Kyrgios’ hopes of playing in his first Grand Slam since a first-round defeat by Britain’s Jacob Fearnley at his home tournment in 2025.
He is next in action on Wednesday in the men’s doubles with Australian-Greek partner Thanasi Kokkinakis, before taking part in the Kooyong Classic warm-up exhibition event in Melbourne next week.
Kovacevic, 27, meanwhile, will face either Britain’s Cameron Norrie or Frenchman Ugo Humbert in the second round.
