The outbreak comes at a time when neighbouring Zambia is battling a cholera outbreak that has claimed more than 67 lives.
Parirenyatwa said that of the 32 cases, two had been confirmed while 30 were suspected in the outbreak reported on Friday.
“We think the index case was an 80-year-old female who succumbed to the disease at home on the 8th of January, 2018,” the minister told a press conference.
Parirenyatwa said some of the people who washed the body of a Muslim woman in preparation for burial were among those who subsequently died.
He said that all the suspected cases were linked to funerals that occurred in the area.
The minister dismissed reports that one more person, a child, had died from the disease, insisting that the death toll remained at four.
He said investigations were continuing to establish whether the outbreak in Chegutu was linked to the Zambian cholera outbreak or not.
Chegutu, like many urban centres in Zimbabwe, suffers from poor water and sanitation conditions, uncollected refuse and uncontrolled vending of foodstuffs which pose the danger of diarrhoeal diseases.
“There is rampant vending in undesignated places, including selling of meat and fruits in pavements.
“People buy and eat all these on the streets in unhygienic conditions, putting themselves at risk of cholera and diarrhea,” Parirenyatwa said.
He urged people in the country to practice good hygiene, avoid big gatherings and shaking of hands at funerals during outbreaks.
Water-borne diseases have become endemic in Zimbabwe’s cities in recent years due to deteriorating water and sanitation conditions.
In 2008, the country recorded its worst cholera outbreak in history when more than 4,000 people died from the disease.