One of the victims died and the other two are now in critical condition.
The three attackers escaped in a Hyundai vehicle from the Imam Hussain mosque in Verulam town on the outskirts of the eastern port city. The motive for the attack was still unknown.
He said it was believed that three men, believed to be Egyptian nationals, were responsible for the attack and fled the scene in a white Hyundai Getz.
Witnesses at the scene claimed the men were Egyptian, and drove away in a Hyundai auto. "Paramedics or doctors who can assist can report to the scene", Rusa said in an earlier statement.
"The attackers managed to get out of the mosque".
The other victims were in critical condition after the attack in the eastern town of Verulam, just north of the city of Durban, South Africa's state broadcaster SABC reported.
IPSSDurban attack A bloodied knife outside a mosque following a deadly attack
The Ethekweni Fire Department was on the scene.
South Africa has a history of relative religious tolerance.
He said a third victim had been attacked inside the building and had jumped out of a window when it was set alight. About 1.5% of the country's population is Muslim.
Speaking further, the representative noted that there had already been theft and robbery incidents at the mosque before.
The attack came shortly ahead of the Muslim fasting month of Ramadan, which begins around May 16.
Beukman said "everything" should be done to arrest the perpetrators and he called on anyone who has information about the attackers to contact the police.