|Abubakr Shekau, leader Boko Haram|
A trader in the north-eastern town told Reuters news agency that Boko Haram fighters took the children with them when they fled.
Troops from Niger and Chad seized Damasak earlier in March, ending months of control by the Islamist militants.
A regional force has recently been helping Nigeria take on the insurgents.
'Helping' is an interesting choice of words. Damasak was won by troops from Chad and Niger, no mention of Nigerian troops. If recent history is any indication, Nigerian troops couldn't take an empty outhouse.
The senator representing the north of Borno state, Maina Maaji Lawan, told the BBC's Nigeria correspondent, Will Ross, the case in Damasak was typical and many hundreds of children are missing.
He said: "The very young ones they give to madrassas… and male ones between 16 and 25, they conscript them and they indoctrinate them as supply channels for their horrible missions."
No mention what they do with the girls, but I think we already know. God have mercy on them!
Boko Haram caused international outrage in April 2014 after it abducted more than 200 girls from a boarding school in Chibok town in north-eastern Nigeria's Borno state.
The group's leader Abubakar Shekau has said the girls have been married off.
|Chadian soldiers drive in the recently retaken town of Damasak|
Regional troops have played a key role in recapturing territory from Boko Haram
|A girl stands in front of soldiers from Niger and Chad in the recently retaken |
town of Damasak. The group is opposed to children receiving a
secular education, alleging that it corrupts their religious beliefs
It was overrun by the militants, who began their insurgency in 2009 to create an Islamic state, at the end of last year.
Damasak businessman Malam Ali, whose brother is among those missing, told the BBC Hausa Service that young boys had been put in a madrassa, or Islamic school, by Boko Haram when they took over the town.
Following the recapture of the town, those boys had not been accounted for, he said.
The BBC's Will Ross reports from Nigeria's main city, Lagos, that the conflict has torn many families apart.
As towns have changed hands it has been impossible to work out how many people have been killed and how many are missing, he adds.
Last week, the decomposing bodies of more than 70 people were discovered under a bridge near Damasak the town.
It is widely believed that these were civilians killed by the militants, our correspondent says.
Boko Haram promotes a version of Islam which makes it "haram", or forbidden, for Muslims to take part in any political or social activity associated with Western society.
Earlier this month, the group pledged allegiance to Islamic State militants, who control large parts of Syria and Iraq and are also active in Libya.