The fire broke out at 26 Broad St. shortly before 4 p.m.
The state fire marshal said a woman was injured and was taken to a local hospital.
Her current condition is not known, reports NBC Boston.
At the time of filing this report, firefighters were attacking the fire from all sides of the building.
The residents of the area said the fire appeared to be just a little smoke until it rapidly grew, engulfing the building.
A local media reported that firefighters from at least a half-dozen communities responded to the scene.
Another report said that a disaster action team is headed to the scene.
Built in 1860, the wood-frame building has 18 units and houses 28 people.
Officials have blocked off several streets in the area, and drivers have been asked to take alternate routes. (ANI)