It is believed to be the first time that a member from the affluent city-state has featured prominently in one of ISIS's videos.
In the English-language video released Saturday, a man identified as "Abu 'Uqayl" from Singapore took issue with Prince Harry talking about a terror attack in London while on a visit to Singapore in June.
"Why don't you come here and fight us if you're man enough, so that we can send you and your Apaches to hellfire, biidhnillah (Allah permitting)?" he said in the video which was circulated by the SITE Intelligence Group.
Prince Harry formerly served in the British army and flew Apache attack helicopters in Afghanistan.
The royal's visit to the city-state in June was overshadowed by an ISIS-claimed terror attack in London.
The attack saw knife-wielding men mow down and stab revellers on a night out, killing seven before they were gunned down by police.
Singapore's interior ministry said it believed the person in the video was a Singaporean.
"Our security agencies have been aware for some time now of the presence in Syria of a Singaporean, Megat Shahdan bin Abdul Samad, 39, and have been monitoring his activities," the Ministry of Home Affairs said in a statement.
"It is believed that the person in the video calling himself 'Abu Uqayl' is Shahdan."
Singapore's leaders have warned that the city is a prime target for a terror attack because of its strong stand against terrorism and reputation