Fungi are eukaryotes. Also Bacteria are prokaryotic cells; protozoa, algae, plants, and animals are composed of eukaryotic cells. Viruses are not cells so they are neither prokaryotic nor eukaryotic.
Fungi are all eukaryotic, it means they have DNA in nucleus, and have membranous organelles in the cell like endoplasmic reticulum, Golgi apparatus, lysosomes, mitochondrial etc..