Nikita Lobintsev, Vladimir Morozov and Daria Ustinova were ineligible for Rio as their names appeared in the recent World Anti-Doping Agency (WADA) Independent Person report, added the world body.
The International Olympic Committee ruled on Sunday not to impose a blanket ban on Russian athletes due to the country's doping history, allowing sports federations to decide on individual cases.
However, it said that athletes who have been sanctioned in the past for doping will not be eligible.
"FINA acknowledges and supports the IOC’s position in respect of the participation of clean Russian athletes to the Olympic Games in Rio," the swimming body said in its statement.
Efimova, who trains with the University of Southern California in Los Angeles, was disqualified from competing by FINA between October, 2013 and February, 2015 after testing positive for traces of the anabolic steroid DHEA.
The 2012 Olympic bronze medallist, in the 200m breaststroke, returned from her ban last year and won 100m gold at the world championships in Kazan, Russia, in August as well as a 50m bronze.
The 24-year-old also tested positive for Meldonium this year but FINA dropped charges against her earlier in July and said she was free to compete.
Efimova's agent Andrew Mitkov told Russian media before FINA's statement that the swimmer would appeal to the Court of Arbitration for Sport if denied the chance to compete at the Games.
The possibility of Efimova competing in the Rio Olympics was already a major talking point in the sport.
Lithuania's Olympic 100 metres breaststroke champion Ruta Meilutyte said last year, after being beaten by Efimova at the world championships, that she could not see the Russian as "a true honest competitor any more".
Relay swimmer Lovtcova was handed a two-and-a-half year ban for doping in 2013, backdated to November 2012. Krapivina collected a five-month ban in October 2013.
(Reporting by Alan Baldwin; Editing by Ed Osmond)
