According to officials, more than 5,000 pregnant Russian women have entered Argentina in recent months, including 33 on one flight on Thursday.
The national migration agency reported that the most recent arrivals were all in their final weeks of pregnancy.
It is thought that the women want to ensure that their offspring are born in Argentina so they can obtain Argentine citizenship.
Recent increases in arrivals have been attributed, according to the local media, to the conflict in Ukraine.
Three of the 33 women who arrived in the Argentinian capital on one flight on Thursday were detained due to "problems with their documentation," joining three other women who arrived the day before, according to Florencia Carignano, head of the migration agency, who spoke to La Nacion.
She said that at first, the Russian women had claimed they were tourists traveling to Argentina.
"In these cases, it was found that they hadn't come to the area to partake in tourism-related activities. They themselves admitted it.
She claimed that since Argentine citizenship provided more freedom than a Russian passport, Russian women wanted it for their offspring.
"The issue is that they come to Argentina, register their kids as Argentineans, and then they leave. All over the world, our passport is very secure. It gives [passport holders] visa-free access to 171 nations, according to Ms. Carignano.
Additionally, having an Argentine child expedites the citizenship process for the parents. Currently, only 87 countries allow Russians to travel without a visa.
A lawyer for the three women who were arrested on Thursday claimed that because they are being held on suspicion of being "false tourists," they are being "falsely imprisoned.". According to Christian Rubilar, "our legislation does not use this term.".
He continued, "These women are being illegally deprived of their freedom. They did not break any laws governing migration.
The women were later released.
The war in Ukraine was cited by La Nacion as the reason for the sharp increase in Russian immigration, adding that "[Russian women] are attracted by their [right of] visa-free entry to Argentina, as well as the high-quality medicine and variety of hospitals, aside from fleeing war and their country's health service.".
Russian citizens appear to be making a tidy profit from the "birth tourism" industry in Argentina.
For expectant mothers who want to give birth in Argentina, a website in Russian that the BBC came across offers a variety of packages. The website promotes services like custom birth plans, airport pick-ups, Spanish lessons, and savings on the price of stays at "the best hospitals in the Argentinian capital.".
First class packages start at $15,000 (£12,433), while "economy class" packages start at $5,000 (£4,144).
The company claims to be "100% Argentinian" and that its founder has been facilitating birth tourism and providing migration support since 2015.