The trio withdrawn by the ROC had previously been sanctioned for anti-doping violations, which meant they failed to meet the eligibility criteria put in place for Russian athletes by the International Olympic Committee (IOC).
"The UCI, through the Cycling Anti-Doping Foundation (CADF), is in the process of identifying relevant rider samples and is in close dialogue with WADA (World Anti-Doping Agency) to move forward with these cases immediately," the UCI said in a statement, referring to the riders under investigation.
"Three other riders who have previously been sanctioned for Anti-Doping Rule Violations have been withdrawn by the ROC," the UCI said, adding that 11 other Russian riders were eligible to compete at the next month's Games.
The IOC ruled after the McLaren Report than any Russian who had been sanctioned before could not compete, even if they had served their penalty.
The three riders withdrawn are believed to be Ilnur Zakarin (Katusha), who won a stage of the 2016 Tour de France, 2012 Olympic time trial and road race bronze medallist Olga Zabelinskaya and Sergei Shilov who rides at Continental level.
The 26-year-old Zakarin is ineligible to race after previously returning an adverse analytical finding for an anabolic steroid in 2009. He served a two-year ban and returned to the sport in 2011.
Zabelinskaya served an 18-month ban and returned to racing in late 2015, while Shilov's doping positive occurred in 2009.
"In addition, the Cycling Anti-Doping Foundation (CADF) has carried out a careful assessment on the other 11 riders named by the ROC to participate in Rio 2016 cycling events," the UCI said.