(http://news.bbcimg.co.uk/media/images/79424000/png/_79424207_nigeria_damaturu_maiduguri_464.png) Another woman exploded the bomb she was carrying in a bag a few feet away, he added.
It was difficult to know how many people had died as body parts littered the area.
The head of the Borno state Fisherman's Union, who was at the fish market and later visited the local hospital, said more than 40 people had died.
The third blast was at a busy bus station where a witness told the BBC that 12 people could be seen lying on the ground.
But he said he did not know if they were dead or injured or whether the blast had been denoted by a suicide bomber or planted in a vehicle.
Last week, Nigeria's President Goodluck Jonathan said the tide has "definitely turned" against militant Islamists as Nigerian troops and their regional allies recapture territory.
Nigeria's presidential and parliamentary elections have been postponed by six week to 28 March to give troops more time to beat back Boko Haram.
Source: BBC