The fighting was set off by the "assassination" of a nomadic Arab-speaking herder and raged between March 17 and 21 in three villages in the southern fertile region of Moyen-Chari, said the minister, Abdraman Koulamallah.
Relatives and clan members of the dead man, who are based in the drier north of the country, led a punitive raid in the village they believed was responsible for the ambush that led to his death.
The minister said calm had returned Monday.
The clashes, which lasted for seven days and spread to two other villages, resulted in nine deaths among the Arab herders and 14 from the local Sara-Kaba people, including four women and two children, Koulamallah said.
He said 21 people have been arrested and investigations were underway to find the "authors, facilitators and accomplices of these crimes."
In eastern and southern Chad, where many residents are armed, clashes frequently break out as sedentary farmers accuse herders of allowing animals to graze on their land or trample crops.
Most of the unrest occurs in the annual transhumance corridors where vegetation is suitable for both crops and feeding livestock.
Beyond Chad, such ancestral disputes have also become more frequent in Sudan, South Sudan, Central African Republic, Cameroon and Nigeria, where fertile tropical regions border the more arid Sahel strip.