The incident occurred shortly before noon when police said the public transport tram on the number 7 line struck the tourist as she was walking in a pedestrian crossing on the Dübendorfstrasse in Schwamendingen, a neighbourhood northeast of the city centre.
The woman was thrown to the ground and seriously injured, city police said in a statement.
Although alerted emergency services staff arrived quickly on the scene, paramedics found the woman was dead before they could help, police said.
The Tages Anzeiger newspaper said online that according to photographic evidence the tram, which was heading toward the city centre, only came to a full stop after it had completely passed the pedestrian crossing.
Police said the exact circumstances of the accident remained unclear.
Specialists from the Zurich Forensic Institute and the accident service of the city police department launched an investigation into what happened.
Police were seeking information from witnesses who can provide details.
Anyone with pertinent details can call 044117117.
In April this year, a 29-year-old woman, originally from Eritrea, died after falling from a tram on line 7 at its southern terminus at Bahnhof Wollishofen.