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.