It included a picture of a young boy carrying a rifle, identifying him as Huthaifa al-Badri.
The statement did not specify when he was killed. It said he was an elite fighter who was killed while fighting Syrian and Russian troops at a power station in central Homs province.
Al-Baghdadi has been reported killed or wounded several times but is widely believed to still be alive.
Little is known about his family, but a woman and child who were said to be his wife and daughter were detained in Lebanon in 2014.
The Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group has been driven from nearly all the territory it once controlled in Syria and Iraq, though it still maintains a presence in the Syrian desert and remote areas along the border.