According to rescue services, they received a call about the fire at around 12.00.
Currently, traffic in the vicinity of the blaze is limited, the Berlin transport network BVG reports on Twitter.
The causes of the fire are not yet known. Rescuers called on residents of the surrounding residential buildings to close their windows due to heavy smoke. About 60 firefighters are working to put out the blaze.
According to preliminary information, the epicentre of the fire is located in one of the containers adjacent to the large trading hangar.
The largest Vietnamese market in Berlin is located in the eastern part of the city, in the Lichtenberg district. Eight large hangars up to 200 meters in length are located in an area the size of of 24 football fields.
About two thousand stores offer clothes, electronics, food, toys, shoes and bags in the market. There are also restaurants, hairdressers, insurance offices, lawyer services, tax advice and translation bureaus.