The 40-year-old former Barnsley boss was appointed on Feb. 6 on a contract until the end of the 2018-19 season.
"Paul came to us during a difficult period in the season and has conducted himself in an exemplary manner despite results not going as any of us had hoped," said managing director Angus Kinnear in a statement.
"Our objective is to bring in a head coach with more experience who can help us reach the goals we have talked about since we became custodians of the club last summer," he added, saying the Championship side hoped to make a quick appointment.
Media reports have linked the club with former Argentina and Olympique de Marseille manager Marcelo Bielsa, who left Lille last December.
Italian businessman Andrea Radrizzani took control of the club in May last year.
Leeds, three-times English champions, finished the season 13th overall. They won just four games out of 16 under Heckingbottom.
(Reporting by Alan Baldwin, editing by Christian Radnedge)
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