The claim of Tomislav Salopek’s execution appeared on a Twitter account belonging to the branch, known as Sinai Province, according to the SITE Intelligence Group, which monitors global jihadist activity.
The authenticity of the picture could not be immediately verified.
A spokeswoman for the ministry said she had no information.
The Croatian ministry said it was in constant contact with the kidnapped Croat’s family and with the Croatian embassy in Cairo and other relevant institutions in Egypt.
Salopek was taken hostage on a highway west of Cairo, while driving to work in a company auto, on a road where no similar incidents had been recorded before.
Islamic State 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.
Milanovic said Croatian security agencies will continue to try to confirm the veracity of the photograph.
Salopek, 30, who worked for Ardiseis Egypt, a unit of French firm CGG, which specializes in oil-and-gas geology, was abducted in Cairo on July 22.
The group released a video last week saying that Salopek would be killed within 48 hours unless the Egyptian government released Muslim women from prisons.
Tomislav Salopek/Facebook Salope, of Croatia, only went to Egypt “to earn bread for his children”, the man’s father told terrorists.
“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…”
The US on Wednesday said its “thoughts are with his [Salopek’s] family, friends and the Croatian people”, condemning the act, while pointing out also that it has yet to be confirmed.
Croatia has previously said that while it was part of the worldwide coalition against IS in the political sense – as a member of the EU and North Atlantic Treaty Organisation – it had no plans to send troops to fight IS.
Militants stepped up their attacks after Islamist President Mohamed Morsi was ousted in 2013.
An Egyptian affiliate of Islamic State claims to have beheaded a Croatian hostage who was captured last month outside Cairo.
He also says Egyptian President Abdel-Fattah el-Sissi’s government tried to “legitimize itself with a supposed tough stance against home-grown militants” but that his security policy “has been a catastrophic failure”. Since then there has been no contact from the kidnappers and Egyptian security forces have launched an extensive search for Salopek.
In his home town, neighbours described Salopek as a friendly young man who had gone to Egypt to earn a living.
Foreign interests also have been targeted increasingly, including the Italian Consulate, which was hit with a vehicle bomb last month.