The men are believed to belong to an Algerian-based terrorist cell affiliated with al-Qaeda, said Barbosa, marking the first time that alleged terrorism suspects have been arrested in the West African nation.
Bissau is located approximately 700km south of where the French family were murdered, while picnicking on the side of a road outside the town of Aleg.
Mauritanian authorities have identified the two suspects as 28-year-old Sidi Ould Sidna, alias Abou Jendel, and 26-year-old Mohamed Ould Chabarnou, alias Mouslim, said a high-ranking police official on condition of anonymity.
Sidna, the official said, was arrested in 2006 and charged with terrorist activities and links to the Algerian-based network al-Qaeda in the Islamic Maghreb.
Chabarnou had tried to steal a car from a Russian diplomat in Mauritania earlier in the year, the offcial said.
"We are in contact with authorities in Guinea-Bissau to see to the extradition of these men."
Three men are believed to have opened fire on the tourists, the third is believed to have fled to Algeria, said Barbosa, who explained that her information came from discussions with French authorities.
Four people, including two children, were killed on the spot, while a fifth tourist, an adult man, survived the attack and was flown to his hometown in France for treatment.
The killing of the tourists and an attack on a military base in the north of the country two days later, which left three soldiers dead, led to the cancellation of this year's Dakar rally.
Al-Qaeda claimed responsibility for the attacks on the Mauritanian troops and organisers of the rally said they had received directs threats from the organisation.