"The wife of Muammar Gaddafi, Safiya, his daughter Aisha, and sons Hannibal and Mohammed, accompanied by their children, entered Algeria at 08:45 am (0745 GMT) through the Algeria-Libyan border," the ministry said in a statement published by APS news agency, giving no information on the whereabouts of Kadhafi himself.
"This information has been brought to the attention of the United Nations Secretary General, the security council president and Mahmud Jibril, president of the executive council of the National Transitional Council (NTC)," the interim administrative body set up by the rebels fighting Kadhafi for power in Libya, the ministry statement said.
There was no word on the whereabouts of his other children, including Seif al-Islam, his most prominent son, whom the rebels claimed to have captured, together with Mohammed, earlier this month.
Seif al-Islam mysteriously resurfaced, free, days later. But Italian news agency ANSA said Gaddaf'i's youngest son, Khamis, had "almost certainly" been killed on the way from Tripoli southwards to Bani Walid.
The same source said Moamer Gaddafi himself and two of his other sons -- Seif al-Islam and former footballer Saadi -- were hiding south of Tripoli in the town of Bani Walid.
Libya's rebel leadership on Sunday said that Khamis, whose death has been announced several times since the conflict erupted, may have been killed in a clash with rebel fighters in the city of Tarhuna southeast of Tripoli.
Earlier Monday the Algerian foreign ministry published another statement announcing that Foreign Minister Mourad Medelci had met Jibril on the margins of an Arab League meeting, though Algeria has not formally recognised the NTC as the ruling power in Libya.
So far, Algiers has adopted a stance of strict neutrality on the conflict in its neighbour, leading some among the rebels to accuse it of supporting the Gaddafi regime.
A rebel source quoted last week by the Egyptian news agency MENA had reported that a convoy of armoured Mercedes had crossed the border into Algeria, a claim categorically denied by the authorities in Algiers.
Simultaneously, ANSA quoted "authoritative Libyan diplomatic sources" confirming that the four had foundrefuge in Algeria.
Mohammed Gaddafi is the eldest son and the more discreet of the leader's offspring. An influential man in his father's regime, he was head of the Libyan Olympic Committee and also the chairman of Libya's General Post and Telecommunications Company.
Aisha was born seven years laters, in 1977. Her style and blonde hair earned her the nickname of "Libya's Claudia Schiffer". She runs a charity and has acted in various negotiations on her father's behalf.
Hannibal, who was born in 1978, is the family's bad boy. He single-handedly strained Libya's relations with Switzerland after causing chaos in a hotel and received a four-month sentence in France for beating his pregnant girlfriend.
Dubbed the "captain, " Hannibal spent time in the military and was in charge of the National Shipping Company.