Atira Hill, Laterry Smith and Jaidon Hill, 7, were last seen Friday in a car that was later found overturned and burning, CNN said Tuesday.
Timothy Burns, 32, has been arrested on suspicion of arson and was being held at the Copiah County jail for "investigative purposes" in the killings, Jones said.
"This happened to a 7-year-old child, and he did not need to have this visited upon him," Jones said.
The sheriff said investigators think Burns was driving the car and became involved in a crash before setting it on fire.
He said it was not clear yet whether the three victims were in the car when it crashed but investigators do not think the family knew Burns -- who led investigators to the bodies.
Atira Hill's mother, Judith Hughes, said her daughter called her Saturday to let her know she and her son were traveling to meet Smith's relatives. Hughes said her daughter told her nothing was wrong.