Vasyl Myroshnychenko tweeted a picture showing the Russian flag being held up by a spectator during the clash between Russian Kamilla Rakhimova and Kateryna Baindl of Ukraine at Melbourne Park on Monday.
Russian players are allowed to compete in the tournament but only under a neutral flag.
Myroshnychenko wrote: “I strongly condemn the public display of the Russian flag during the game of the Ukrainian tennis player Kateryna Baindl at the Australian Open today. I call on Tennis Australia to immediately enforce its “neutral flag” policy.”
Baindl moved through to the second round with a 7-5 6-7 (8) 6-1 victory.
The PA news agency has contacted organisers for comment.