The 25-year-old Popov, whose sprint freestyle victories in Atlanta gave him recognition as the world's fastest swimmer, was stabbed when a group he was with got into a fight with watermelon vendors in Moscow on Saturday night.
He is hospitalized in stable condition.
Police spokesman Vladimir Zubkov said two Azeris, aged 24 and 28, have been detained in the incident. The stabber has been identified but not apprehended, he said, according to Interfax.
Police said Popov was on his way home from a birthday party with friends when they had an argument with street vendors in western Moscow. Investigators said the fight apparently was initiated by Popov's friends.
Popov has lived and trained in Australia for several years. Many top Russian athletes have tried to escape the woes that have plagued Russia since the Soviet collapse by training abroad.
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