"Our heroic armed forces have eliminated Daesh commander Abu Yaser Al-Issawi as part of an intelligence-led operation," Kadhimi tweeted.
Last week, Islamic State claimed responsibility for a twin suicide bombing which killed at least 32 people in a crowded Baghdad market. It was the first big suicide bombing in Iraq for three years.
Iraqi authorities said the attack was a possible sign of the group reviving after its military defeat in 2017.
Suicide attacks on civilian targets were a near-daily tactic of the mainly Sunni Muslim insurgents during the US occupation of Iraq after the invasion that toppled Saddam Hussein in 2003.
Many of the insurgents were later recruited by Islamic State, whose fighters swept across a third of Iraq in 2014.
By 2017, however, Islamic State insurgents had been driven from all territory they held. Their paramount leader, Abu Bakr al-Baghdadi, died in 2019 during a US raid in neighboring Syria.