Niyonkuru completed the 21-kilometre race in 1:06:08 (a new national record), finishing behind Kenya's Agnes Jebet Ngetich, who set a women-only world record (1:05:15) for gold, and Kenya's Veronica Loleo, who took silver in 1:06:05.
The 25-year-old was the best-performing of Rwanda's three representatives in the race. Emeline Imanizabayo (15th) and Ibishatse Angelique (39th) also competed for Rwanda.
The World Athletics Road Running Championships are organised by World Athletics and were held in Copenhagen.
The bronze adds to Niyonkuru's recent run of strong performances. She finished third in the 10,000 metres at the Commonwealth Games, winning Rwanda's first-ever senior medal at the Games. She also won gold at the TCS World 10K Bengaluru in India earlier this year.
