Customer director Crawford Davidson is believed to have taken on her responsibilities.
Coomber was at Dobbies from 2013 having joined from Standard Life and is due to take on a new high profile marketing role in April.
Davidson joined Dobbies in February after being chief marketing officer at Ideal Shopping Direct. He was previously customer marketing director at Morrisons.
Dobbies chief executive John Cleland left the business on 6 March, with former Wyevale chief Nicholas Marshall taking over.
Tesco bought the 34-centre group in 2007 for £155m and sold Dobbies to Midlothian Capital Partners and Hattington Capital in 2016 for £217m, when Cleland was appointed replacing Andy King.