The murder of a British citizen on the Zrce beach occurred around 05:35 am (0335 GMT), a police statement said.
Police said the identity of the victim, a young man, was known but for now they would not provide further details.
Local media reported that the victim was 26 years old who got involved in a fight in front of a night club.
Selfie gone wrong: Tourist couple dies in Portugal
The northern island of Pag, notably the town of Novalja and Zrce beach, is well known as a summer party destination for young tourists, many of them British.
Tourism is a major industry for Croatia where visitors flock to its stunning Adriatic coast, with more than 1,000 islands and islets.
Last year the country of 4.2 million people welcomed more than 17 million tourists. Among them there were more than 750,000 British visitors.
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