Nimrod the hunter is killed by his bitter rival Esau, who is himself a renowned hunter. Both Nimrod and Esau are so utterly consumed by jealousy towards one another that it's just a matter of time before one of them ends up dead. Unfortunately for Nimrod, this just happens to be him.
One day, while he's out and about in the wilderness, Nimrod becomes separated from his men. This gives Esau, who's been stalking him at a distance, the opportunity to strike against his bitter rival, which he does by cutting off Nimrod's head. For good measure, he wipes out the two men who were with Nimrod.
This is the story as it is recounted in the Book of Jasher, which is part of the Apocrypha, those non-canonical books of the Bible deemed by certain Christians not to be divinely inspired. However, Esau makes an appearance in the Book of Genesis, which most certainly is canonical. Here, the hunter notoriously sells his birthright to his brother Jacob for a “mess of pottage,” which is a kind of stew made from lentils.
Although Genesis and the Book of Jasher may not enjoy the same status among most Christians, their portrayal of Esau is nonetheless consistent.
Many religious scholars agree that Nimrod didn't die a natural death. Jewish tradition says that Nimrod died after a gnat entered his brain and gnawed on it. Some Jewish historians claim that Nimrod suffered from the pain for forty years before he died. Islamic tradition largely supports this interpretation but replaces the gnat with a mosquito.
In the Bible (Genesis 10), Nimrod is described as a mighty hunter. He possessed extraordinary strength and ruled over the kingdoms of Babel, Erek, Akkad, and Kalneh in the land of Shinar. However, there's no discussion of how Nimrod met his end.
Both the Bible and first-century historian Flavius Josephus agree that Nimrod was a rebel leader. Josephus maintained that it was Nimrod who set up the world's first totalitarian government.
Meanwhile, the extra-biblical text of Jasher says that Esau beheaded Nimrod with his sword. Other religious scholars argue that Nimrod was actually murdered by his great-uncle, Shem.
According to this theory, Shem had Nimrod's body cut into pieces and sent out to the nations as a warning against idolatry. Religious scholar Alexander Hislop says that Nimrod was actually Ninus, a Babylonian king.
Hislop wasn't the first to make the claim. Many historians from antiquity and the Middle Ages believed that Nimrod was Ninus and the founder of idol worship. Near the end of the first century, Clement, in his Clementine Recognitions, alleged that the Greeks knew Nimrod as Ninus.
This Ninus, according to Clement, introduced all magic arts to mankind.
As can be seen, there's no consensus on how Nimrod died. That said, religious scholars and historians concede that Nimrod didn't die a natural death, he rebelled against God and taught others to do the same, and he possessed extraordinary height and strength.
The answer to your question can be found in the first seven verses of chapter twenty-seven of the Book of Jasher. This book, although left out of many contemporary versions of the Bible, is mentioned in various other books of the Bible, both in the Old and New Testaments.
Both Nimrod, who was king of Babel, and Esau (well known as the brother of Jacob) enjoy going hunting. A rivalry has formed between the two, with Nimrod being jealous of Esau. The fifth verse reveals that while they come across each other in the hunting grounds that day, Esau makes himself scarce.
However, when Nimrod and his men come close, Esau emerges from his hiding place, presumably taking Nimrod and his men by surprise. He draws his sword and beheads Nimrod without a moment's hesitation.
Of course, Esau then has a battle on his hands, because two of Nimrod's men are also present. Nimrod's other men hear the battle noise from a distance and run to see what happened. Esau, however, doesn't wait around to see what happened next. He makes his escape, taking with him the valuable garments that Nimrod had been wearing.
Later in the chapter, we are told that Nimrod's men bring his body back into the city and bury him.
The Book of Jasher 27:1-9 describes the death of Nimrod by saying that there was jealousy between him and Esau, the son of Isaac and brother of Jacob. Both of them would hunt in the same field and one day Esau saw Nimrod and his companions coming, hid, and then jumped from his hiding place catching Nimrod by surprise and killed Nimrod and his companions. It says "and (Esau) drew his sword, and hastened and ran to Nimrod and cut off his head." (*The Book of Jasher is an apocryphal book referred to in Joshua and First Samuel.)
There are a number of traditions as to how he died.Some say that he was killed by wild animals and others say that Shem, the son of Noah, killed him because he was leading the world into idolatry.The Jewish Encyclopedia states that Nimrod lived a wicked life as one of the world's first emperors. An angel from God appeared to him and strongly urged him to repent.
"But Nimrod declared that he himself was sole ruler and challenged God to fight with him. Nimrod asked for a delay of three days, during which he gathered a considerable army; but this was exterminated by swarms of gnats. One of these insects is said to have entered Nimrod's nose, reached the chambers of his brain, and gnawed at it."
Nimrod would die after 40 years of struggling with the pain from the gnat embedded in his nose..