Tennis Australia did not provide details, but a video emerged on social media showing a fan on the steps of Rod Laver Arena holding up a Russian flag with the image of President Vladimir Putin on it.
Russian and Belarusian flags are banned from Melbourne Park during the Australian Open after a complaint from the Ukraine ambassador to the country last week.
Belarus is a key staging ground for Russia's war in Ukraine, which Moscow terms a "special operation".
"Four people in the crowd leaving the stadium revealed inappropriate flags and symbols and threatened security guards. Victoria Police intervened and are continuing to question them," Tennis Australia said in a statement.
"The comfort and safety of everyone is our priority and we work closely with security and authorities."
Photos on social media also showed one fan in the crowd during the quarter-final with a large "Z" on his shirt.
Russian forces have used the letter "Z" as an identifying symbol on their vehicles in Ukraine following the invasion. Some supporters of the invasion have also used the sign.
Ukraine's Former player Alexandr Dolgopolov urged Tennis Australia to issue a life ban for the individual in a tweet.
Vasyl Myroshnychenko, Ukraine's ambassador to Australia and New Zealand, posted a picture last week showing a Russian flag hanging from a bush beside a court where his compatriot Kateryna Baindl (28) was playing her first-round match.
Tennis Australia responded by immediately banning the flags of Russia and Belarus.
Russian and Belarusian players were banned from Wimbledon last year but are able to compete as individual athletes without national affiliation at the Australian Open.
Their flags are not displayed beside their names in TV broadcasts, as is the case for other players, and their nation is not indicated on draw sheets.
