The agency was awarded the business without a competitive pitch and is now charged with helping the United Nations Population Fund (UNFPA) to raise money and awareness of the condition that affects more than two million women worldwide.
Its debut creative work is expected to include a TV element along with promotional activity and sponsorship initiatives. It will initially be focused on the UK and Europe.
James Murphy, the managing director at RKCR/Y&R, said: "Fistula is a medical condition that devastates lives and yet it can be reversed with a simple operation costing a few hundred dollars. We will deliver a simple idea to drive the entire global campaign."
The UNFPA was launched in 1969 to push for obstetric health for women in developing countries. It unveiled its first campaign to prevent and treat fistula last year.
Micol Zarb, a UNFPA spokeswoman, said: "We were impressed with RKCR/Y&R's creative track record in raising awareness of sensitive health and human-rights issues affecting women and their communities."