Those who do not have coupons have been asked to deliver 700 litres of fuel.
One teacher at Petra High School said it was cash-strapped parents who originally wanted to pay in kind.
Though politicians in Zimbabwe signed a power-sharing deal last week, the country is still suffering from an acute economic crisis.
The last official figure given for annual inflation was 11,000,000%. Last month the central bank struck 10 zeros from the currency, making 10bn Zimbabwe dollars equal to one new dollar.
Banks only allow people to withdraw a maximum of 1,000 new Zimbabwe dollars a day.
"If you are paying school fees of 100,000 dollars, that means I will be going to the bank for the next five months to withdraw 1,000 dollars until I reach the requirement amount for fees," said one parent, Babongile Simanga.
Petra High School was not available for comment but two teachers confirmed that if parents failed to raise enough cash, they could pay in whatever they have, including livestock.
It is not clear how many parents have handed over animals, but the practice is said to have been going on for some time.
"It’s not only Petra High school that is doing that," said Dumisa Tshabalala of Magwegwe township, who has two children at Embakwe High School in the neighbouring province of Matabeleland South.
"Many schools these days are doing it and we should blame the government not schools."
Cows are the usual method of payment because of their higher value, though poor people in rural areas have also used goats.
Zimbabwe has been suffering from chronic inflation
Another teacher at Petra High said the decision to ask parents to improvise was taken at a meeting with the school development association.
Most of the parents who attended are said to have agreed because of the cash shortages, but some are now complaining and calling for teachers to be dismissed.
One problem is how to determine the market value of the animal, since cattle sales have ceased amid Zimbabwe’s economic crisis.
Themba Sithole, an official for the Progressive Teachers Union of Zimbabwe, criticised schools demanding fees in the form of livestock or fuel coupons.
"The question here is who is benefiting from this practice. Is it the school or individual teachers or heads?" he asked.
But Eunice Sandi, a former Zanu-PF senator for the Bulilima constituency, said schools should not come under fire.
"We must not blame schools when they ask us as parents to find ways of beating the cash crisis," she said.
Meanwhile, teachers are demanding that the government pay them US$1,200 a month – or about Z$48,000.
Currently teachers earn Z$1,200, which is about $US35 on the local parallel market.