The fires have occurred in the city's Mitchell Park and Barron Park neighborhoods, Palo Alto police Agent Dan Ryan said.
There have been 22 arson fires reported since January, he said.
Items lit on fire have included a bench, a construction site outhouse, garbage cans, and papers inside a restroom at the Cubberley Community Center, Ryan said.
Ryan said there is no evidence the fires are connected but that they remain under investigation.
The most recent fire, which Ryan said may have been accidental, was reported at about 9:10 p.m. Wednesday at Bol Park in the 3500 block of Laguna Avenue.
Ryan said a small patch of grass was burning along a jogging trail, and witnesses reported seeing people smoking there just before the blaze started.
No one has been injured in the fires, but Ryan said, "We are taking this very seriously to prevent anything from happening."