Walker, 71, now an independent MSP, was this week convicted of 23 charges of assault against three former wives and a teenage step-daughter.
His former brother-in-law Rob Armstrong said he gave court documents to a staff member in Glasgow MSP Ms Sturgeon's parliamentary office in February 2008, years before Walker was elected.
Labour has called for a full account of Ms Sturgeon's role in the discovery of Walker's history of domestic abuse.
Jackie Baillie, the party's social justice spokeswoman, said: "It is imperative Nicola Sturgeon comes clean as to why she took no action when confronted with the original allegations against Walker.
"I sent her a list of 20 questions to get clarity on the series of events that took place and she has failed to answer a single one."
But Ms Sturgeon hit back last night, when she said: "Mr Armstrong met a member of my staff and as his complaint was a party matter, the matter was quite correctly referred to SNP HQ, where an investigation was conducted.
"As it did not relate in any way to my work as a constituency MSP, I was not made aware of the situation.
"My constituency office gets a very large volume of contacts from people who are not constituents but who want to raise party issues. As my staff are not employed by the SNP, these matters are rightly passed on to the party. The member of staff who spoke to Mr Armstrong acted absolutely appropriately.
"The investigation conducted by a member of staff at SNP HQ did not find any evidence of any complaint in law or legal proceedings into domestic violence by Mr Walker, and the inquiry was then closed."
Mr Armstrong had said the worker "photocopied certain newspaper articles and advised me she would pass this on to the executive and I should expect to hear from someone in the executive in due course. I never heard anything further."
When asked if the documents contained "hard evidence" about Walker's past, he said. "Yes. There was also the judgment of a Swindon court, where a judge described William George Walker as a tyrant and a bully."
SNP MSP Linda Fabiani said Ms Sturgeon's constituency office acted "absolutely correctly" in passing the information to headquarters. She said: "We're not the police. We know Bill Walker is a consummate liar. He denied everything in court."
Walker will be sentenced on September 20.