Owen is to become director of Shop Direct Group's Very brand, which was launched in 2009. He will report into Shop Direct retail director Gareth Jones in his new role.
"Jon has left for a bigger job," an Asda spokeswoman confirmed. "We will appoint someone else in due course but there is no timetable in place." She added that there was no-one lined up to replace him.
Owen had replaced Mark Sinnock as marketing director, who held the role for 15 months. His departure is the second high-profile exit at Asda in as many weeks. COO Simon King unexpectedly left last week by "mutual consent" after just six months. Asda is expected to announce a successor to King shortly.