Those deemed ineligible for Rio include Yulia Efimova, a 200m bronze medallist in London, who had a provisional ban lifted by Fina last week, BBC reports.
It said the McLaren Report has showed anti-doping rules were “not properly applied” by Russian authorities.
Fina will also now re-test all the samples of Russian athletes collected at last year’s World Championships.
As well as Efimova, Mikhail Dovgalyuk, Natalia Lovtcova and Anastasia Krapivina were withdrawn by the Russian Olympic Committee.
Nikita Lobintsev, Vladimir Morozov and 17-year-old Daria Ustinova appeared in the World Anti-Doping Agency-commissioned investigation.
That report by Dr Richard McLaren claims Russia operated a state-sponsored doping program for four years across the “vast majority” of summer and winter Olympic sports.
Following the findings, the International Olympic Committee (IOC) said it would leave it up to individual sports’ governing bodies to decide if competitors are clean and should be allowed to take part.
Fina said it “acknowledges and supports” the IOC’s position.
Fina will, therefore, “as a decision made as an emergency in the context of Rio 2016” subject the eligibility of Russian athletes to specific additional criteria, which are:
Fina said the “exact implication for the Russian Swimming Federation is still to be clarified” and an “ad hoc commission will have to investigate”.
The commission will consider any further information from McLaren’s ongoing investigation.