Alex Salmond said Walker, 71, was "not fit to be a public representative" after being convicted of "extremely serious offences".
The First Minister was one of a number of politicians who called on Walker to resign as MSP for Dunfermline.
The independent MSP was convicted of 24 charges spanning almost three decades following a trial at Edinburgh Sheriff Court.
Walker, who lives in Alloa, carried out the attacks against his three ex-wives - Maureen Traquair, Anne Gruber and Diana Walker - and Mrs Gruber's stepdaughter Anne Louise Paterson between 1967 and 1995.
The former SNP MSP, who was ejected from the party when the allegations surfaced, had denied the charges.
Mr Salmond said: "Mr Walker has been convicted of extremely serious offences.
"Although he has yet to be sentenced, in my view someone convicted of these offences is not fit to be a public representative and therefore he should stand down from the Scottish Parliament and allow the people of Dunfermline to elect a new MSP."
The SNP leader added that Walker was expelled from the party in April last year, and said: "His conviction by a court of law reinforces his expulsion."
The law says that any elected member jailed for more than a year will be disqualified from being a member of the Scottish Parliament.
Claire Baker, Labour MSP for Mid Scotland and Fife, said: "Whatever sentence is handed down by the court, the Scottish Parliament cannot have a member who has been convicted of 23 counts of domestic abuse."
She added: "It has been reported that Nicola Sturgeon and the SNP hierarchy knew of the allegations of Bill Walker's violence against women as early as 2008, and yet he was still selected to represent the SNP in 2011.
"Nicola Sturgeon and the SNP leadership must now tell the people of Scotland who knew what and when."
A Scottish Conservative spokesman said: "It's astonishing the SNP thought this man was fit to be an MSP after Nicola Sturgeon's office was informed of a number of allegations against him."
Walker will be sentenced on September 20.