Toronto Transit Commission spokesman Brad Ross says a rider complained to the driver about lewd behaviour taking place on a packed streetcar at about 5:30 p.m. Thursday.
He says the operator stopped the vehicle and called in a report but the couple fled before police and transit officials could arrive.
The car was taken out of service for what the TTC called a "security incident" but was back on track about 15 minutes later.
Referencing the Tennessee Williams masterpiece, Ross quipped that "every streetcar in Toronto is named desire," but said the allegation has not been confirmed.
"I can't independently verify that the act itself happened, but somebody...claims that they saw it," said Ross, adding no investigation is underway by the transit agency.
Toronto police said they have received no report of the alleged incident.
Ross says such complaints are very rare, adding that it's a big system that operates 24 hours a day and there might be some people "who can't wait to get home."
But he said people should keep in mind that the transit system is a public place.
"People from all walks of life ride the system, including children, and we would ask that people who are using the system who wish to get to know one another a little bit better do so in the privacy of their own home or somewhere other than on a streetcar."
The incident generated its own hashtag on Twitter (#torontostreetcarsex) with many people posting racy comments and others sharing their disgust.