Surveillance video initially caught the animal roaming Gaven Street in the city's Portola District, around 3:50 a.m., according to San Francisco Animal Care and Control officials.
Later Tuesday morning, an eyewitness reported seeing the mountain lion near Bernal Hill Park.
As a precaution, officials with the San Francisco Recreation and Park Department posted warning signs throughout the park, cautioning residents and visitors to be on the lookout.
VIDEO: Mountain lion stares through window into Scotts Valley home
Animal Care and Control officers have also been deployed the area, but, according to Animal Care and Control spokesperson Deb Campbell, for now, there's no plans to capture the animal.
"Either it's hunkered down under a bush, waiting to get out of town, or it's already gone," she said. "Mountain lions are pretty elusive. They don't want to bug people."
Residents who encounter mountain lions are encouraged to avoid running or turning their back. Instead, they should face the animal, make noise, try to look bigger by waving their arms, throw rocks or other objects, and pick up small children. Additionally, dog owners should keep their dogs on a leash.
Anyone who spots a mountain lion is encouraged to call the SF Animal Care and Control emergency dispatch line at (415) 554-9400.