Talbot, who is understood to have joined online cycling specialist Wiggle, was leading a review of the site's advertising arrangements.
With his replacement yet to be appointed, the review, which was being handled by Creativebrief, is now on hold.
Chief executive John Perkins, who joined Play.com in April, is responsible for the internal restructure. Perkins was previously senior director for northern and southern Europe at Apple.
Play.com claims to be the UK's third-most-visited online retailer, behind Amazon and eBay.
However, it faces increased competition from rivals including The Hut Group, which recorded a 188% year-on-year increase in the number of orders placed in the six weeks to Christmas 2009. The Hut Group also owns the Zavvi brand, which it acquired in March 2009 and relaunched as an online brand.
Talbot had planned to embark on a long-term £4m umbrella brand campaign to run across TV, press, outdoor and digital media, in an attempt to fend off this threat.
Previously, Play.com has used ad agency Libertine on a project basis. A retained agency was scheduled to be appointed by the end of April.
The brand has used marketing to highlight its price promotions, and its shift from selling mainly DVDs, CDs and video games to offering a wider range of products.
In February, the site hired Jason Mather, who was formerly a senior marketer at Warner Bros, in the new post of head of product marketing.
Play.com was unavailable to comment on Talbot's departure or the advertising review as Marketing went to press.