Zaire broke off relations with Cuba today, charging that a Cuban diplomat based here had been found with "irrefutable evidence" of Cuba's involvement in the Katangan rebellion in Zaire's southern Shaba Province.

No specifics on the evidence were made available.

A communique from Zaire's official news agency said security forces had caught a Cuban attache, M. Fernandez, in the act of demonstrating Cuba's collusion in the month-old "invasion." It also charged that Fernandez was an espionage agent.

The Cuban diplomatic staff has been given 48 hours to leave the country, and Zaire has recalled its officials from Havana.

Relations have been tense between the two countries for the past 18 months because of Angola's civil war. During the conflict Zaire provided bases and, briefly, troops for the pro-Western Front for the Liberation of Angola and Cuba sent an estimated 20,000 troops to help the victorious Marxist faction, the Popular Liberation Movement.

Hostility was open after March 8 this year, when Katangan rebels crossed over from bases in Angola and started to push across the mineral-rich region that is Zaire's economic lifeline. Zaire army officials have charged several times that Cuban troops were leading and fighting with the Katangans, although no proof has ever been produced.

During his recent tour of Africa, Cuban President Fidel Castro denied that his forces were helping Katangan rebels, who now control a third of Zaire's Shaba province. Cuban troops, estimated to number up to 20,000 are still backing the government in Angola, however.

At the Cuban embassy, a white villa in the wealthy area of Kinshasa, staff members were seen throwing papers into a fire in the courtyard.

The Cubans have been in Zaire less than three years.

The Zaire government has made another major move related to the rebellion by sacking its chief of staff, Capt. Gen. Bumba Moaso Djigo, and replacing him with Maj. Gen. Babia Zonghi Malobia, according to diplomatic sources.

The move reveals the government's dissatisfaction with the army effort to contain the rebels, who are apparently moving deeper into Shaba Province without serious resistance.

The change in army commanders comes at a crucial point, as guerrillas are within a few miles of Kolwezi, Zaire's mining center. Loss of the town would have seriouseconomic and political repercussions.