Dobbie joined the retailer from a consultancy role at Mother, Asos’ previous ad agency.
Asos later appointed Bartle Bogle Hegarty to its advertising account without a pitch after the online retailer and Mother ended their relationship in autumn last year.
Dobbie reported to Asos chief executive Nick Robertson and was a member of the operating board while at the company.
A spokeswoman for the brand would not confirm whether it had lined up a replacement for Dobbie.
Before consulting for Mother, Dobbie was responsible for setting up Gap’s European marketing team as vice-president of marketing for Gap Europe and also launched Gap-owned Banana Republic in London.
Dobbie began her career in advertising and worked on brands including Nike at creative agency Simons Palmer, now part of TBWA.
She left agency-side to become marketing communication director at Nike UK, overseeing the launch of Niketown before joining French Connection as marketing director.
Marks & Spencers' clothing and homewares business head Kate Bostock is in talks to take up a senior position at Asos, according to reports.
Last month Asos posted a 66% rise in first-half profit on the back of strong sales growth overseas.
Asos.com marketing director Clare Dobbie has parted ways with the online fashion retailer after joining the company in March last year.