Reuters could not independently verify the authenticity of the picture, which carried a caption that said: "killing of the Croatian hostage, due to his country's participation in the war against Islamic State, after the deadline expired ... ".
If confirmed, it would be the first known beheading of a Western hostage held by Sinai Province, the Egyptian group which changed its name from Ansar Bayt al-Maqdis after it pledged allegiance to Islamic State.
A spokesman at the Egyptian Interior Ministry's press office said: "We have seen this news on line but are currently making our own checks. If we confirm that it is indeed true, we will inform the media through a statement."
The Croatian embassy and foreign ministry declined to comment. Prime Minister Zoran Milanovic was due to hold an extraordinary news conference at 5 pm.
The photograph, circulating on Twitter accounts of Sinai Province supporters, shows a man's severed head placed on his body, with a knife driven into sand next to it and the black Islamic State flag in the background.
Next to the picture are screenshots of Arabic language news articles with the headlines: "Croatia confirms its support for Egypt in efforts to fight terrorism and extremism" and "Croatia affirms its continued support for the Kurdistan region."
Last week, an online video purportedly from Sinai Province showed a man who identified himself as Tomislav Salopek who said the group would kill him in 48 hours if Muslim women in Egyptian jails were not freed.
Ardiseis Egypt, a unit of French oil and gas geology company CGG, confirmed the video showed one of its employees who was kidnapped on July 22 while travelling to Cairo.
A spokesman for CGG could not confirm this, adding the firm had no information other than what was circulating on the Internet and was trying to find out more from Croatian and Egyptian authorities.
The spokesman said the hostage was an expert contractor rather than employee of its subsidiary.
Last December, Sinai Province said it was behind the killing of an American petroleum engineer whose body was found in a car in a desert region almost four months earlier.
Sinai Province is at the forefront of an Islamist militant insurgency in Egypt that has killed hundreds of soldiers and police in the two years since the military ousted Islamist President Mohamed Mursi after protests against his rule in 2013.
In July, the group was involved in the deadliest fighting there in the lawless Sinai Peninsula in years, in which more than 100 militants and 17 soldiers were killed, following simultaneous assaults on military checkpoints in North Sinai.
Islamic State, which has captured vast swathes of Iraq and Syria, has over the past year beheaded an unknown number of hostages, both Western prisoners and Middle Easterners ranging from soldiers fighting it to Muslims who reject its hardline version of Islam.