While other species including gibbons and long-tailed macaques have also been spotted crossing there, "this is a world first for Sumatran orangutans," it added.
The bridge's use by the orangutan was a "huge milestone for conservation", SOS chief executive Helen Buckland said.
"These canopy bridges demonstrate that human development and wildlife don't have to be at odds. Sometimes, the simplest solutions are the most effective," Buckland added.
The road is an important social and economic link for communities in Sumatra's Pakpak Bharat district.
But it has also split a population of some 350 orangutans, SOS said.
Erwin Alamsyah Siregar, executive director at Tangguh Hutan Khatulistiwa, said that habitat fragmentation was "one of the greatest challenges in contemporary conservation".
He said he hoped canopy bridges would become a "standard feature" of infrastructure planning across the region.
The International Union for Conservation of Nature classifies Sumatran orangutans, endemic to the island of Sumatra, as critically endangered.
Their decline is blamed on habitat loss and fragmentation as well as illegal hunting.
In the wild, orangutans are found only on Sumatra and the nearby island of Borneo, which is shared between Indonesia, Malaysia and Brunei.