Abu Hussein al-Qurayshi is believed to have taken over the group after his predecessor died in a raid in February.
Mr Erdogan told broadcaster TRT Turk the IS leader was "neutralised" in a Turkish MIT intelligence agency operation on Saturday.
IS has so far made no comment on the reported operation.
The BBC has been unable to independently verify President Erdogan's claim.
The MIT intelligence agency had been following Qurayshi for a "long time", Mr Erdogan said.
"We will continue our struggle with terrorist organisations without any discrimination," he added, providing no further details.
Syrian sources quoted by Reuters news agency said the operation took place in the northern town of Jandaris, close to the Turkish border.
In February, then-IS leader Abu Ibrahim al-Hashimi al-Qurayshi set off a blast killing himself and his family as US special forces rounded on his hideout after a gunfight.
That operation "removed a major terrorist threat to the world", US President Joe Biden said at the time.
In November, the jihadist group announced the death of its leader, Abu al-Hassan al-Hashemi al-Qurayshi. The US said he was killed in an operation by the rebel Free Syrian Army in south-west Syria in mid-October.
IS once held 88,000sq km (34,000sq miles) of territory stretching from north-eastern Syria across northern Iraq and imposed its brutal rule on almost eight million people.
The group was driven from its last piece of territory in 2019, but the UN warned in July that it remained a persistent threat.
It is estimated to have between 6,000 and 10,000 fighters in Syria and Iraq, who are based mostly in rural areas and continue to carry out hit-and-run attacks, ambushes and roadside bombings.
IS regional affiliates also pose threats in other conflict zones across the world. The UN said the most vigorous and well-established networks were based in Afghanistan, Somalia and the Lake Chad basin.