The incident occurred at Gel River in Awerial County.
The injured included a 30-year old Ayen Malith and a boy identified as Mabor Majeuc.
The two were fishing when tragedy struck. They are receiving treatment at Awerial County hospital.
John Jool, the clinical officer in charge of the hospital, said the reptile was trapped in a fishing net.
He said the injuries were minor, but expressed concerns over the absence of essential drugs.
The administrator for Mabor Jila Boma, Ganoon Ayat Kon advised residents on safety measures.
“There are many aquatic creatures like crocodile and snakes that live in Gel as their home. The current fishing method of using mosquito nets is unsafe. Previously, people used fishing nets, spears, and hooks to catch fish and that was safer than using mosquito nets,” stressed Kon.
He, however, urged residences to prioritise safety measures while fishing.