"Palestine will be free, Palestine will be free," hundreds chanted during their march.
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Hundreds of protesters marched down Market Street, towards bustling Union Square, calling for an immediate end to the war between Israel and Hamas.
Traffic had come to a halt near Powell Street at around 1:30 p.m., where the protesters encountered police.
MORE: Protesters who shut down Bay Bridge demanding for cease-fire in Gaza call on SF DA to drop charges
At one point police advised shoppers to avoid the area after demonstrators became rowdier.
According to police, the group then moved to Union Square, where "several people began to commit crimes," ranging from assault to felony vandalism, a spokesperson for the San Francisco Police Department said. The department said there was property damage as well.
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Demonstrators vandalized monuments and holiday decorations.
Graffiti was written throughout Union Square but police were able to disperse the crowd.
A photo of a protester climbing the Union Square Christmas tree with a sign could be seen on the social media platform X, formerly known as Twitter.
Several people were arrested, and as of 8 p.m. the group appeared to have left Union Square, police said, though officers remained in the area.
"We are not confirming the exact number of arrests or the charges due to the active investigations," SFPD said in a statement.
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The Christmas tree in Union Square was dark Saturday night. It was not clear if it was a result of the protest.
Bay City News contributed to this report.