The bird had a ring on its leg reading "Hungary Budapest" and a yellow ribbon around its neck with the mark 10 JJ, spokesman Mladen Pavic said.
Croatian ornithologists will get in touch with their Hungarian colleagues to establish where the swan had come from, Pavic told Hina.
Samples from the killed swan were sent for analysis to the Poultry Centre at the Zagreb Institute for Veterinary Medicine.
There is no danger for humans because all poultry in the area has been killed, Pavic said.
Last week an H5 avian influenza virus was discovered in six swans at the Grudnjak fish farm.
The head of the veterinary service in the neighbouring town of Nasice, Darko Damjanovic, reported the successful completion of an operation to cull poultry in the area of the local fish farm "1905", which started this morning.
Ministry spokesman Pavic said that some 10,000 head of poultry were killed in the operation, which covered 400-450 households in five settlements in the Nasice area.