The flight, which was carrying 74 passengers and four crew, was due to travel to Geneva.
"The pilots rejected take-off at low speed due to an engine problem and subsequently evacuated passengers and crew safely," a Swiss spokeswoman told AFP.
The airline said four passengers "received on-site treatment by the ambulance services for minor injuries".
The plane was a British-made four-jet Avro RJ100 regional airliner, the company added.
The runway at London's City Airport, which predominantly serves business routes in Europe, was closed for about an hour while the aircraft was cleared, an airport spokeswoman said.
Britain's Air Accident Investigation Bureau said they had deployed a team to "investigate a serious incident" at the airport.