Anthony Roko, a 20-year-old volunteer firefighter, was taken from the field on a stretcher before being transfered to a clinic that specialises in hand injuries.
The match, which Nice won 2-1, was held up for several minutes as police officers picked up pieces of Roko's fingers from the field.
The bomb had been thrown from the area of the stand where the Marseille supporters were sitting, when the match was just five minutes old.
Agricultural bombs are usually used to make holes in the ground.
Local leader Christian Estrosi condemned the throwing of the bomb as "a criminal and stupid act."