Nzuza was stabbed to death in full view of congregants attending a church service on Friday.
She was allegedly stabbed by her husband.
"The death of a councillor who is an elected servant of the people leaves a gaping void in the sphere of local government and has robbed us of one more foot soldier in our fight against poverty, inequality and unemployment," Dube-Ncube said in a statement.
"It appears that this tragedy which cast a shadow over Easter festivities in the community of Indaka was prompted by domestic violence which the provincial government condemns with equal force."
She said such incidents were a reminder that domestic violence remained a grave challenge in communities.
Police spokesperson Jay Naicker said the stabbing followed an argument between the two.
"The suspect asked her to return back home as she left him due to the domestic argument. The victim refused, then the suspect fatally stabbed her," he said.
The man later handed himself over to Ekuvukeni police.