In a response to a tweet asking if the prominent right-wing conspiracy theorist's account would be reactivated, Musk quoted a bible verse and indicated he wouldn't be allowing him back.
"Suffer little children, and forbid them not, to come unto me: for of such is the kingdom of heaven," tweeted Musk.
He then added a personal note about one of his children, perhaps suggesting that Musk sympathizes with the parents whose kids were murdered in the Sandy Hook shooting.
"My firstborn child died in my arms. I felt his last heartbeat," continued Musk. "I have no mercy for anyone who would use the deaths of children for gain, politics or fame."
Jones has denied that the 2012 school shooting took place and claimed it was a hoax. Earlier this month, a judge ordered Jones to pay $1.4 billion to the families of the children that died.
According to Business Insider, Musk's son died in 2002. The infant was found not breathing when his former wife went to wake him up. The child spent three days on life support, and later died.
Some criticized Musk's decision not to reinstate Jones' Twitter account, saying Musk was picking and choosing and creating the policy as he goes.
On Saturday, Musk reinstated the account of Donald Trump, reversing a ban that kept the former president off Twitter since a pro-Trump mob attacked the U.S. Capitol on Jan. 6. Musk made the announcement after holding an online poll that asked Twitter users whether Trump should be allowed back.
Musk said Friday his new Twitter policy will allow for freedom of speech, not freedom of reach.
He recently reinstated controversial Twitter users Kathy Griffin, Jordan Peterson and the Babylon Bee.
The bustle comes amid a mass exodus of employees after Musk gave staff two days to decide whether "to be extremely hardcore" or leave.
As of Thursday, many said "challenge accepted" and left. Reuters reports hundreds have resigned.