PM Zoran Milanovic addressed the nation after an Egyptian jihadist group claimed it had killedTomislav Salopek, who was seized three weeks ago.
A photo purporting to show his body was posted on Twitter by a user associated with the group calledSinai Province.
It earlier threatened to kill him unless Egypt freed jailed Muslim women.
The photo circulated online on Wednesday shows a decapitated body in what appears to be desert, beside a knife driven into the sand and the black banner used by IS.
The caption says the Croatian, a father of two aged about 30, was killed “for his country’s participation in the war against Islamic State”.
He had been working as a surveyor for French geoscience company CGG, which is involved in the oil and gas industry.
Mr Salopek was seized while travelling about 22km (14 miles) west of Cairo on 22 July, security sources said.
If the death is confirmed, it would be the first time that jihadist militants in Egypt have beheaded a Western hostage since stepping up their campaign against the state two years ago.
Frantic search
The Croatian government could not confirm Mr Salopek’s death “with 100% certainty”, Prime Minister Milanovic said.
“I am not sure if we will be in any position to confirm the news in the next few days, but what we can see doesn’t look good, it looks very bleak… I am afraid that the worst has happened.”
Mr Milanovic urged people not to share the gruesome image posted online.
He also stressed that Croatia would not take part in combat operations against IS.
Croatia has previously said that while it was part of the international coalition against IS in the political sense – as a member of the EU and Nato – it had no plans to send troops to fight IS.
Analysis: Frank Gardner, BBC security correspondent
There is no official confirmation that Tomislav Salopek has been murdered, but his abduction marks a new and dangerous development in Egypt’s evolving security situation.
While the northern half of the Sinai Peninsula has been home to violent jihadists for some years now, this is the first time that a foreigner has been abducted in Egypt, and not far from the outskirts of Cairo.
The men who stopped Tomislav Salopek’s car at gunpoint on 22 July were said to have had Bedouin accents. It is possible that he was then sold on to IS.
The Egyptian authorities mounted a frantic search for his whereabouts but there are vast, unpopulated areas of Egypt’s desert where he could have been taken and hidden. It is even possible that he was taken over the border into Libya where there is no effective national government.
Whatever the precise details, this could have grave implications for Egypt’s future ability to attract foreign investors.
A week ago, Sinai Province posted a video of a man who identified himself as Mr Salopek kneeling in the desert next to a masked militant holding a knife.
The man said the Egyptian authorities had 48 hours to comply with Sinai Province’s demands about female Muslim prisoners or face death.
Since the 2013 military overthrow of President Mohammed Morsi, as many as 40,000 Muslim Brotherhood supporters and other Islamists are believed to have been detained and more than 1,000 others killed in a crackdown.
Sinai Province has also claimed it was behind the killing of the American petroleum engineer William Henderson, whose body was found in a car in the Western Desert in August 2014.
The jihadist group was known as Ansar Beit al-Maqdis until it pledged allegiance to IS in November and changed its name.
Militants belonging or linked to IS have carried out or claimed a series of killings of Western and other hostages over the last year or so. They include US journalists James Foley and Steven Sotloff, and British aid workers David Haines and Alan Henning.
Scaling back?
CGG, the French geoscience company that employed Mr Salopek, has said it may scale back its operations in Egypt as a result of the apparent murder.
Spokesman Christophe Barnini told the BBC the company was in talks with its clients “about the level of risk they are willing to take and that we are willing to take”.
Mr Barnini refused to comment in detail on the circumstances of Mr Salopek’s abduction but said the company had since increased its security measures.
Apache, the US firm that employed William Henderson, said on Wednesday it had “various security measures in place” in Egypt but would not discuss them for safety reasons.
BP, which employs thousands of people in Egypt, also declined to comment on security but said it was “closely monitoring the situation”.
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