Hamburger rejoined in a board-level marketing director role last month from T-Mobile, where he was senior director for end-user marketing. The retailer brought him back as part of a bid to overtake market leader Carphone Warehouse.
Despite being responsible for the launch of its £8m marketing campaign based on the 'Phones4Less' theme, Neal has decided to leave the retailer.
Phones4U said it had offered Neal a number of alternative roles, but he had opted to move on.
Neal does not have another job to go to and is undecided whether to stay within the mobile phone industry.
Phones4U is understood to have instigated a review of its creative account, which is currently held by Cheetham Bell JWT.