The celebrations reportedly turned violent after fans lit several fires across the city.
Police reportedly arrested a few people as the streets filled with revellers who threw water bottles at officers. Some fans also reportedly jumped on top of buses prompting services on city streets to be halted.
Police spokesman Gordon Shyy said: “Police personnel were assaulted with bottles on Market Street and Mission district. Officers in the Southern district were also struck with bottles. These objects were thrown at officers as they attempted to disperse crowds and assist firefighters extinguish bonfires.”
Police officials, some in riot gear, reportedly tried to calm the crowds marching down the streets. Some fans also spray-painted walls. Police said the injuries of the two shot people were not life-threatening.