The revelation emerged as it was reported last night that Derek Hyslop had threatened to expose his criminal past in an attempt to blackmail Ms Jamieson when she was serving as education minister.
Ms Jamieson said her nephew had threatened to sell the story of his criminal career to the newspapers in the past if the minister did not pay.
In 2001 Hyslop sent a Christmas card to his aunt demanding money while he was in jail for manslaughter.
But the minister went straight to the police and only revealed the relationship last night in an interview.
She said: "I received a Christmas card from him, but was shocked to find a note in it saying that if I didn’t give him money he would make sure my political opponents found out about him.
"I couldn’t believe it - after all we had done for him. I immediately took the note to the police and they dealt with it.
"I know what it is to be a victim of crime and I know the pain decent families feel when they have a family member who is a criminal."
The nephew was originally charged with murder but convicted of manslaughter in England.
Hyslop was recently released on licence from a prison after serving four years for his crime, according to reports.
He had spells in residential care and was locked up as a teenager at Polmont Young Offenders’ Institute in Stirlingshire and at Glenochil in Clackmannanshire.
Ms Jamieson told how she did everything she could to help her wayward nephew go straight, even taking him into her family home and giving him money.
But she said she had to turn him into the police after he took the family Ford Escort and wrote it off and stole one of her colleague’s cars.
It is understood that Hyslop is now claiming that the money given to him by the Carrick, Cumnock and Doon Valley MSP was to help him evade the police.
In the interview, she said that the motivation behind her tough stance on violent crime was the fact that she had a criminal in her own family.
And after experiencing the frustration of a close family member stealing from friends, vandalising her own property and even blackmailing her, Ms Jamieson said it has driven her to help other families across Scotland.
The minister, who last week announced a raft of measures against antisocial behaviour, said: "I am not proud of my nephew.
"No family is proud of having a criminal amongst them. But I have never tried to hide the truth.
"I have always tried to help him get back on the right path. He is one of the reasons I feel so strongly that we have to crack down on criminals."
Ms Jamieson was unavailable for comment last night.
The Executive said the alleged blackmail attempt was the minister’s personal family matter. Strathclyde Police said last night it was unaware of any complaint.
Ms Jamieson is currently pushing for a new Police Bill that would introduce new powers for police and courts to crackdown on criminals.