Evans, who now lives in Nigeria, was visiting a sister in the San Francisco area when the tumor on his pituitary gland was discovered, the San Jose Mercury News reported.
In 1968, Evans, now 63, was one of the "Speed City" runners from San Jose State University. He and his teammates made history with the medals they picked up in Mexico City and with their open political activism. Tommie Smith and John Carlos, who won gold and bronze in the 200 meters, gave Black Power salutes from the podium.
Evans won gold medals in the 400 meters and the 1,600-meter relay in 1968. He and his relay teammates wore black berets like those worn by the Black Panthers during the medal ceremony.
Carlos announced Evans' illness in an e-mail to other Olympic athletes.
"All of our teammates want to go out and say some prayers," Carlos said. "There's not too much we can do but pray."
Evans, who is married to a Liberian refugee, is trying to raise money for a school outside Monrovia. He moved to Africa to work for the United Nations after leaving his job as a coach at the University of Alabama in 2008.