Police say the men spoke to the pair once they realised what had happened but later fled.
Otago Fish and Game CEO Ian Hadland said any firearms incident is a tragedy and he is saddened to hear about it.
Hadland said he wasn't sure if the hunters have come forward yet but they need to.
"We really need to get to the bottom of the incident and the circumstances around it so we can better understand what went on there.
"If there is any way we can avoid incidents in future, we'd be desperately interested to find out about that."
Hadland said the hunters have obviously broken one of the seven basic rules.
"They didn't identify their firing zones. There's a chance that they were aware of the firing zone and people have inadvertently walked into it but in any case, it's the firearms users' responsibility to be sure of their firing zone and that obviously hasn't happened here."