Park authorities said the incident took place at Burhapahar range of the park, a Unesco world heritage site.
"Gun shots were heard from the park and our forces launched an operation immediately. There were four poachers who managed to escape after retaliation by the forest guards. We have recovered the carcass with the horn," said a park official.
Poachers have been using sophisticated weapons to kill rhinos, he said.
"We have recovered empty cartridges of AK-series rifles and a night-vision scope attached to a rifle, which the poachers might have dropped," he said.