The trio refused to put on their bikini tops when approached by officers at Necochea, the Atlantic coastal resort in Buenos Aires. One even whipped her top off when being warned about their behaviour.
The women say the police called to the scene threatened to arrest them during a heated discussion on the sand watched by bewildered sunbathers.
The three friends eventually agreed to leave but only after police called in reinforcements over fears that the argument could escalate.
Row over three topless sunbathers brings 20 police to beach
Although going topless in Spain has been accepted for years, it still raises eyebrows in Argentina and is not the norm.
At one stage, the discussion became very heated
The three women took off their tops on the popular beach but a number of other tourists were said to have been offended by the "exhibitionism" and called in the police.
The trio alleged they were being picked upon and said they had as much right as a man to go topless.
The row eventually involved other beach users, some of whom agreed with their stance, others who objected. At one stage, about 20 police officers in six patrol cars arrived.
The trio refused to put on their bikini tops when approached by officers at Necochea
"At one stage, the discussion became very heated," one onlooker told the Spanish press. "A police officer apparently told them to put their breasts away as people were fed up seeing them. They were also told to go away and find a proper nudist beach."
The women only agreed to move away after the police said they would put them in handcuffs.
The angry scenes were caught on video by numerous tourists and has reopened the debate about topless sunbathing in the south of Argentina. The footage has been posted on Youtube and has already gone viral.
Women's groups are now calling for protests in various parts of Argentina next week, including on the beach itself.
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The angry scenes were caught on video by numerous tourists
The women have found one major supporter in the form of the Mayor of Necochea, Facundo Lopez. He said telling the trio to cover up was "a violation" but "what happened afterwards could not be justified" as it was not worthy of a row.
"The law is obsolete, I am ready to modernise it. Just look at the comments in the networks to note that there is still a long way to go to eliminate machismo in Argentina."
Websites have been set up so other women can register their objections and marches are to be held on February 7 and 11.
One of the protests is being planned for the famous obelisk of Buenos Aires under the motto "Our breasts should not be censored!"