North Kivu regional governor Nzanzu Kasivita Carly said there had been deaths, but did not give a number.
The plane crashed into houses in the Mapendo neighbourhood after "missing" its take-off from the city's international airport, he added.
Residents on the ground were among the casualties, local media reports said.
The Dornier-228 aircraft was owned by private carrier Busy Bee.
It was supposed to fly to Beni, 350km (220 miles) north of Goma, when it came down about a minute after take-off, a source at Goma airport told the BBC.
The North Kivu governor said he was sad to confirm that the crash had "cost the lives of our fellow countrymen", and he offered his condolences to the families of survivors.
Air accidents are relatively frequent in DR Congo, amid lax safety standards and poor maintenance.
All the country's commercial carriers are banned from operating in the European Union.