Sheriff Charles Jones says in a news release that Kendel Montgomery is the grandson of the victim, 68-year-old Mary Webb of Davenport.
Jones says Montgomery was arrested Tuesday in Memphis, Tenn. He says Webb's vehicle also was found in Memphis.
Jones says Montgomery is being held in the Coahoma County jail pending an initial court appearance.
Jones says the 68-year-old Webb suffered multiple stab wounds. He says an autopsy is being performed.
Jones says family members found Webb's body underneath her bed in her trailer Sunday.
The case is still under investigation.