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, Clackmannanshire, carried out the attacks against his three ex-wives and a stepdaughter between 1967 and 1995.
The former SNP MSP, who was ejected from the party when the allegations surfaced, had denied the charges but was convicted after a two-week trial.
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.
"Bill Walker should stand down now. His vile conduct over many years will disgust Scots and shames the Scottish Parliament.
"I would like to commend the bravery of his victims who were prepared to relive the pain of many years so that justice could be done."
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."
Scottish Green Party co-convener Patrick Harvie said: "It is deeply concerning that the Scottish Parliament finds itself facing the possibility that a member convicted of serious domestic abuse charges might be able to continue to sit, depriving a constituency of proper representation and drawing a salary from public funds.
"Clearly, Walker should resign immediately. If he doesn't have that single shred of decency there must be an immediate debate about changing Holyrood's rules to allow the removal of a member convicted of such serious offences.
"If there has been no resignation by the time Parliament next meets, I will be seeking that debate."
Walker will be sentenced on September 20.
Scottish Liberal Democrat leader Willie Rennie said: "What sort of message would it send to victims of domestic abuse if Bill Walker was allowed to keep his seat in Parliament despite his conviction?
"He has to go and he has to go now."
An SNP spokesman said that, under party rules, it had been Walker's "inescapable responsibility to inform the party's candidate assessment panel of information that has come to light, which he completely failed to do, and of course he even denied in a court of law".
He also said a former brother-in-law of the MSP had visited Ms Sturgeon's constituency office in February 2008, where he had spoken to a member of staff.
The spokesman said: "As this discussion did not relate in any way to the work of Ms Sturgeon's constituency office, the staff member quite properly informed party headquarters of the points made - Nicola Sturgeon was not made aware of this.
"The matter was considered by a member of staff at SNP headquarters and reasonable inquiries made, but there was no evidence of any complaint in law or legal proceedings into Mr Walker's conduct, and the inquiry was closed."
He said that, after Walker's expulsion from the party last year, SNP president Ian Hudghton MEP had carried out an internal review of assessment procedures.
The spokesman said: "While the onus was clearly on Mr Walker to disclose information, which he did not do, in a significant strengthening of our procedures any potentially relevant information made available to party headquarters will be passed directly to the Election Committee convener for assessment.
"The breadth of coverage on the question of any matter that could cause concern for the party has also been expanded.
"The candidate application form asks for full transparency on any past or current civil proceedings, tribunals or professional body disciplinary action, as well as past criminal charges, whether resulting in a conviction or not, and any current police investigations into the applicant's conduct."
Scottish Conservative leader Ruth Davidson said: "The truth of the matter is that a family member of one of Bill Walker's victims informed the party hierarchy of serious allegations of violence made against him, yet the party still saw fit to put him in Holyrood under the SNP banner.
"The SNP leadership now has some big questions to answer in relation to the way in which they have handled this whole unsavoury episode."
Walker was elected to the Scottish Parliament in a surprise victory for the SNP two years ago.
On a night of success for the party, Walker, now 71, beat the previous Liberal Democrat winner into third place and finished 590 votes above Labour.
But his Dunfermline seat now hangs in the balance.
The law states that any elected member jailed for more than one year will be disqualified, forcing a by-election.
Walker has consistently refused to resign from Parliament since the allegations first surfaced in the Sunday Herald newspaper on March 3 last year.
He was suspended by the SNP and stepped down from his positions on two Holyrood committees.
Later that month he used a column in the Dumfermline Press newspaper to describe the claims against him as "malicious allegations".
By April, he was expelled from his party. Police became involved later that month.
Despite growing calls for him to leave Holyrood, including pressure from campaigners against domestic abuse, he clung on to his seat as an independent member.
Increasingly isolated in the debating chamber, he was not asked to join a new group of other independent and Green MSPs.
Police announced his arrest on June 8 2012 and he made his first court appearance on July 5 that year.
Walker was born in Edinburgh and has a background in electrical engineering.
As a politician, he has argued against plans for same-sex marriage.