Quan said the park, which is located above state Highway 13 in the Oakland hills, "is an attraction for kids from all over the Bay Area to have campfires and drink and do whatever teenagers do."
She said there are many parties in the park during the graduation season and the summer.
Quan, who was joined by police and fire officials at a news conference at the park, said Joaquin Miller Park is "unique" because "it's a 500-acre forest in the middle of the city."
City officials are concerned about campfires because they could spark a forest fire, she said.
Hikers occasionally find embers from campfires in the park and there were at least three smoldering fires there last summer, according to Quan.
People who go to the park late at night face fines of up to $500 and could face fines of up to $1,000 if they start campfires, she said.
Oakland police and fire officials said they will be conducting increased patrols late at night to try to keep people out of the park.
Quan, "We want to give a warning to young people" to stay out of the park late at night.