The latest arrivals were all in the final weeks of pregnancy, according to the national migration agency.
It is believed the women want to make sure their babies are born in Argentina to obtain Argentine citizenship.
The number of arrivals has increased recently, which local media suggests is a result of the war in Ukraine.
Of the 33 women who arrived in the Argentine capital on one flight on Thursday, three were detained because of “problems with their documentation”, joining three more who arrived the previous day, migration agency head Florencia Carignano told La Nacion.
The Russian women had initially claimed they were visiting Argentina as tourists, she said.
“In these cases it was detected that they did not come here to engage in tourism activities. They acknowledged it themselves.”
She said the Russian women wanted their children to have Argentine citizenship because it gave more freedom than a Russian passport.
“The problem is that they come to Argentina, sign up their children as Argentinean and leave. Our passport is very secure across the world. It allows [passport-holders] to enter 171 countries visa-free,” Ms Carignano said.
Having an Argentine child also speeds up the citizenship process for parents. As it stands, Russians can travel visa-free to only 87 countries.
Travel to many Western countries has become more difficult for Russians since their country invaded Ukraine last February.
Last September, the visa facilitation agreement between the EU and Russia was suspended, resulting in the need for additional documentation, increased processing times and more restrictive rules for the issuing of visas.
A number of countries have also suspended tourist visas for Russians, including all EU member states that border Russia.
A lawyer for the three women who were detained on Thursday said that they are being “falsely imprisoned”, as they are being held on suspicion of being “false tourists”. This is a term “which does not exist in our legislation,” Christian Rubilar said.
“These women who didn’t commit a crime, who didn’t break any migratory law, are being illegally deprived of their freedom,” he added.
The women have since been released.
La Nacion attributed the dramatic uptick in arrivals of Russian citizens to the war in Ukraine, saying that “besides fleeing war and their country’s health service, [Russian women] are attracted by their [right of] visa-free entry to Argentina, as well as by the high-quality medicine and variety of hospitals”.
“Birth tourism” by Russian citizens to Argentina appears to be a lucrative and well-established practice.
A Russian-language website seen by the BBC offers various packages for expecting mothers who wish to give birth in Argentina. The website advertises services such as personalised birth plans, airport pick-ups, Spanish lessons and discounts on the cost of stays in “the best hospitals in the Argentinian capital”.
The packages range from “economy class”, starting at $5,000 (£4,144), to “first class”, starting at $15,000 (£12,433).
The website says its founder has been facilitating birth tourism and offering migration support since 2015, and the company says it is “100% Argentinian”.
On Saturday, La Nacion reported that Argentine police had been carrying out raids as part of an investigation into a “million-dollar business and illicit network” that allegedly provided pregnant Russian women and their partners with fake documents issued in record time to allow them to settle in Argentina.
Police said the gang charged up to $35,000 (£29,011) for the service.
No arrests were made, but police were said to have seized laptops and tablets, as well as immigration papers and significant quantities of cash.
