The collision took place late Monday in the Issy-les-Moulineaux suburb southwest of the capital just after 9:00 pm (2000 GMT).
"The one in front was stopped, and the other crashed into it from behind," causing the first tram to derail.
"One victim is in serious condition, and 11 others have minor injuries," a spokesperson for the fire department said, adding that nine of the victims had been brought to local hospitals.
Traffic was "entirely cut off" during the night, and bus services were put in place as repair work was carried out at the site of the crash.
RATP chief executive Catherine Guillouard visited the scene overnight, saying "an internal enquiry was immediately triggered in order to shed light on the causes of this accident." Traffic is expected to be disrupted for several days as the repair work is carried out, the RATP said.
Accidents are rare on the busy Paris suburban tram network, which was opened two decades ago.
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