Two people have so far been confirmed dead, but Ould Vezzaz could not confirm how many more were still missing.
"I appeal to international solidarity, notably our development partners," he said.
"The situation is under control, but we are facing problems with food, safety, electricity and providing drinking water, since the water supply network was washed away by the violent tide of water."
Qatar's official news agency QNA quoted on Sunday a source at the foreign ministry as saying that Sheikh Hamad bin Khalifa Al Thani, the country's ruler, had ordered relief assistance to be sent to Mauritania urgently.
Ould Vezzaz said schools, health facilities, roads and market places were also damaged or destroyed.
He said the authorities were looking for alternative sites to rebuild houses for residents prepared to move from low-lying districts.
Seasonal rains have arrived across large swathes of West Africa in the past few weeks, giving relief to rural farmers who can now plant their crops, but also bringing devastation to some low-lying and densely populated areas.
Mauritania lies at the western edge of the Sahara and is mostly arid for much of the year, except during the seasonal summer rains which can be torrential.