The aid agency can provide medical help, but has no food to give them.
Until now Somalis have been pouring across the borders to Ethiopia and Kenya, arriving at giant refugee camps which are severely overcrowded.
Joe Belliveau of MSF told the BBC the development of camps inside Somalia was a "most desperate and vulnerable moment."
This is a rare glimpse of the situation inside Somalia itself.
MSF is one of a few aid agencies still managing to operate in those areas of Somalia controlled by the militant Islamist group, al al-Shabab.
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"Just about a week ago, the number there was about three hundred families in that camp. Within the space of a few days that has jumped to eight hundred families," he said.
Mr Belliveau explained that when people left their homes and their wider families and begun to cluster in camps it indicated that their ability to cope had been exhausted.
"And that's why you see such an outflux also into Ethiopia and Somalia because people have just reached the point, which is the most scary point, where they no longer are able to cope with backup measures for survival," he said.
Mr Belliveau said the recent statement by al-Shabab lifting its ban on aid agencies working in areas it controls was welcome, but so far it had made no difference on the ground.
MSF is having the greatest difficulty in getting permission from al-Shabab to airlift materials into Somalia and bring in expatriate staff.
Africa editor, BBC World Service