The government said circumcision was one of its key strategies for "achieving an AIDS-free generation" in Rwanda, where around 210,000 people are living with HIV.
Non-surgical circumcision involves a plastic device called PrePex comprising two rings and an elastic band that cuts off blood supply to the foreskin, which shrivels and is removed with the band after a week.
Minister of Health Agnes Binagwaho said it had been "clinically validated as a bloodless procedure that doesn't necessitate injected anaesthesia".
"Rwanda is the first country to launch non-surgical adult male circumcision with an aim of reducing HIV infection," Binagwaho said at the launch of the project, which is backed by the World Health Organisation.
The health ministry said it "aims to circumcise 700,000 adult men between ages 15-49" by the end of 2016.
"Studies have shown that circumcision reduces the risk of heterosexually acquired HIV/AIDS infection by roughly 60 percent," the ministry said in a statement, adding that "male circumcision is one of the key strategies to achieving an AIDS-free generation."
The makers of PrePex boast that a man "can resume work and almost all daily activities shortly after the procedure", with the device "designed to be placed, worn, and removed with minimal disruption", although they should abstain from sex for six weeks afterwards.
The device takes only five minutes to apply. Tzameret Fuerst, president of PrePex, described it as "a very simple procedure that any nurse can conduct."
Rwanda's adult HIV rate of 2.9 percent is already quite low compared to some other African nations.
As well as Rwanda, the PrePex device is already also being used in Botswana, Kenya, Mozambique, South Africa, Uganda, Zambia and Zimbabwe.