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Wragg was appointed customer director - a new position - in late 2013.
He had previously headed up the multichannel division.
Wragg was heavily involved in developing the retailer's Click & Collect service along with Asda's app.
According to the retailer, he departed the company as he wishes to return to working in a senior multichannel position.
Steve Smith, Asda's chief customer officer, paid tribute to Wragg in a memo.
“Jon has been with us since 2006 building a great career across George, operations, trading, multichannel and most recently within my marketing team."
“He accepted the customer director role as part of a restructure in December, with an important caveat that he wanted to keep his options open to get back into a multichannel/eCommerce role should one become available.”
“I, and the entire Asda board, are sad to see Jon leave, but he departs with our gratitude and respect as a trusted, generous and productive leader of the organisation.”
Asda has now begun the search for a new customer director.