Lee Eun-ju of South Korea and Hong Un-jong of the North took a quick smiling snapshot during the training period before the start of the Games.
The pictures of the two women have been widely praised as capturing the Olympic spirit.
North and South Korea are technically still at war with each other.
And relations between the two have been more tense in recent months, with recent missile launches from Pyongyang.
"This is why we do the Olympics," tweeted political scientist Ian Bremmer. His tweet was retweeted more than 18,000 times.
"Sports brings everyone together," said another user on Twitter.
Others hailed it as the "most iconic photo" of the games.
Some users however, took a more cynical point of view.
"Is she allowed to fraternise with the enemy?" was one such question asked, while others questioned whether Hong might face punishment on her return home.
Lee, 17, and 27-year-old Hong both competed as individual qualifiers, with the games in Brazil being Lee's first Olympics, BBC reported.
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