He ran over two women doctors who were riding on a motorcycle before he was caught by police, the official said.
The unnamed suspect was shot by police five times and is undergoing surgery at an island hospital, said Chrysanthos Roussos, head of the Santorini district on the island.
Initially, the man roamed the village of Vourvoulos exhibiting the woman's head, Roussos said.
When a policeman tried to handcuff him, the suspect knifed the officer and flung the victim's head into a patrol car, Roussos said.
The suspect then made off in a second patrol car and ran over the motorcycle before he was caught, Roussos said. The two doctors suffered multiple fractures, Roussos said.
The suspect, from northern Greece, was reported to have worked at a local restaurant.
The victim, said to be in her mid to late 20s, was a teacher in a local village, Angelos Roussos the mayor of Thira, the island's main town, was quoted as saying by TV station Antenna. Angelos Roussos and Chrysanthos Roussos are not related.
Police refused comment.