Washaya-Moyo said no arrests have been made and investigations were in progress. Rangers recovered 1kg (2.2lb) of cyanide and are increasing patrols in the park, she said. Cyanide is widely used in Zimbabwe's mining industry and is easy to obtain.
Rangers in Zimbabwe are struggling to protect elephants from poachers who are using cyanide.
Last week rangers in the country's Hwange national park discovered the carcasses of 26 elephants at two locations, dead of cyanide poisoning along with 14 other elephants which were found the week before, The Guardian reports.
This comes after around 300 elephants were killed in the park after drinking poisoned water in 2013.
Patrolling rangers discovered the carcasses last Tuesday, according to the Bhejane Trust and the National Parks and Wildlife Management Authority. The Bhejane Trust undertakes joint animal monitoring and welfare work with the parks agency.
A parks spokeswoman, Caroline Washaya Moyo, said 14 tusks had been recovered from these elephants but the others had not been recovered. She said rangers had found 16 of the elephants in the Lupande area and 10 others in Chakabvi.
No arrests made
"The poachers were probably disturbed by rangers on patrol, which is why some of the tusks were recovered. Cyanide poisoning is becoming a huge problem here and we are struggling to contain it," said Trevor Lane, a founder of the Bhejane Trust and a leading wildlife conservationist.
The environment, water and climate minister, Oppah Muchinguri, blamed the increase in poaching on a US ban on hunting Zimbabwean elephants for sport.