The incident occurred shortly after 4.30pm as a number 15 tram was travelling north on the Weinbergsrtasse toward Schaffhauserplatz, police said in a news release.
Shortly before junction with the Leonhardstrasse, a number 7 tram using the same rails rear-ended the number 15 tram for reasons not immediately known, the release said.
The crash occurred in an area of the city on the east side of the Limat River not far from Zurich's main train station.
Emergency services staff looked after eight of the injured passengers, while the passenger transported to hospital needed treatment for “moderate injuries” to the knee, a police spokesman told the SDA news agency.
Police said the crash caused 100,000 francs' damage.
Specialists from the city force are investigating the cause of the accident.
A section of the Weinbergstrasse between the Central and Leonhardstrasse areas was closed while investigators and rescue services staff dealt with the aftermath of the collision.
“On impact a very loud bang was heard,” a witness told the 20 Minuten newspaper.
Ironically the accident occurred on the same day that the Zurich transit authority (VBZ) advertised on its website its “safe” and carefree transportation services, including trams, for partygoers on New Year's Eve.