He was arrested on Saturday in Mississippi on unrelated charges.
The children, ages one to eight, were reported missing on Wednesday, when their mother told police she could not get in contact with her ex-husband.
Wilcox County, Alabama, District Attorney Michael Jackson told the AP the father is suspected of killing the five children in Lexington County, South Carolina, and dumping the bodies in Alabama.
Authorities found the children buried near an Alabama highway after an all-day search on Tuesday, local media reported.
Jones was first named by Mississippi officials.
Smith County, Mississippi, Sheriff Charlie Crumpton told the Clarion Ledger newspaper that Mr Jones was stopped at a safety checkpoint on Saturday and was determined to be driving under the influence of drugs or alcohol.
When officers ran his vehicle's identification through a national database, he was listed as a missing person.
Mr Jones had told neighbours in South Carolina he was preparing to move out of the state with the children, local media report.