The video shows a man wearing a yellow jumpsuit who is kneeled in front of a masked militant holding a knife.
The video is believed to come from Isis's Egyptian affiliate group in the Sinai Peninsula.
The man reads aloud from a note, identifying himself as 30-year-old Tomislav Salopek. He says ISIS captured him on 22 July.
He said he will be killed if Egyptian authorities do not give in to the demands within 48-hours, although it is not clear exactly who the group wants released from prison.
Croatia's Foreign Ministry confirmed that one of its nationals had been kidnapped in Cairo last month.
Mr Salopek said he worked for CGG Ardiseis, a French oil and gas company that have an office in a Cairo suburb which are home to many expats and diplomats.
The title of the footage was “A Message to the Egyptian Government”.
Militants from the extremist group have carried out a number of beheadings in the past, releasing footage of the killings as part of its propaganda.
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