Police and firefighters responded to a blaze on the east end of the park, located at 2901 Cowper St., at about 11 p.m. on July 7.
Authorities arrived to find a children's jungle gym fully engulfed in flames, police Detective Brian Philip said.
Firefighters extinguished the fire as quickly as they could, but the play structure was destroyed.
Residents in the area told police they saw juveniles in the park just before the fire. Investigators are working to determine whether the fire was arson, Philip said.
The city of Palo Alto and the nonprofit Friends of the Palo Alto Parks are offering a combined award of $2,000 for information about the fire.
Police urge residents to report any suspicious people or activity occurring in the city's parks.
Anyone with information about the fire can call Palo Alto police at (650) 329-2413 or e-mail anonymous tips to email@example.com.