The council has adopted the policy after consultation with women's aid groups. It is thought to be the first in the UK to use such strong measures against workers convicted of domestic violence offences.
The council's stance is contained in a new policy document which warns that where there is a 'conflict between the conviction for domestic violence and the job the employee is employed to do some form of disciplinary action may be taken'.
Council workers who are victims of domestic violence are also being offered help in the form of counselling, time off and other aid. The issue is also being introduced into the school curriculum.
Ms Scott said: 'For example, where you have a teacher of personal and social development who was teaching children about domestic violence as part of the curriculum, and he or she was found guilty in court of that offence, then there would be a conflict of credibility.'
Unions said they supported the move in general but there were questions about what affected someone's working capability and whether the policy could be extended to include those convicted of racist abuse and other crimes.
A spokesman for Unison said: 'We support what the council is trying to achieve in principle but we don't want this to be used to undermine the rights of staff.
'If someone has been dealt with through the courts then why should they be placed in double jeopardy by then being penalised by their employer?'