The murders took place in Arafat, a suburb of the capital Nouakchott where the man, a public sector nurse in his forties, lived with his family.
Sources close to the family, speaking on condition of anonymity, said the man had waited for his wife to leave their home on Thursday night, before slitting the throats of his two sons and two daughters.
The eldest was 12 and the youngest less than a year old.
One of the sources said that upon her return, the mother found her husband smiling and he said to her: “I have gotten rid of your concerns about buying clothes for the children for the holiday.”
Those close to the family said the nurse suffered from “psychological problems.”
The man has been arrested, and a policeman said he had confessed to having killed the children as he could not afford to buy them new clothes, a tradition during Eid, a holiday which marks the end of the Muslim fasting month of Ramadan.
The holiday will fall on either Monday or Sunday in Mauritania depending on lunar cycles.
The quadruple infanticide has horrified residents of the capital who cannot recall a crime of its nature in recent history.