The Top Gear host issued the warning after writing about his partner Frances's participation in the Ironman Triathlon last weekend in aid of Help for Heroes.
"Right. Today my wife is swimming 2.4 miles, cycling 112 and then doing a marathon," he wrote. "And if any troll out there thinks it'd be "funny" to be rude, I will find you and I will kill you."
Clarkson continued to jest with his followers later, announcing that he was taking "drastic measures" to see his wife at the Bolton event before tweeting a picture of a private helicopter.
After Frances completed the race, Clarkson proudly revealed: "In case anyone is interested, my wife did her 2.4 mile swim, 112 mile bike ride and 26 mile run in 16 hours, 52 minutes. Quite incredible."
The presenter is known for his controversial comments, which include suggesting that long delays at UK border control could be solved by "a bit of racism" and calling for striking public sector workers to be shot.