Anna Maria Cancellieri is accused by critics of using her influence to help ensure Giulia Ligresti, who reportedly suffers from anorexia and anxiety, was moved from prison to house arrest.
She will testify before the two houses of parliament , according to Italian media reports.
"I will not resign, my conscience is clean," she was reported as saying by Italy's La Repubblica daily.
"I made a humanitarian intervention based on the possibility that an inmate could have died," Cancellieri told RAI television, after published transcripts of her phone calls appeared to show her promising the Ligresti family she would deal with the matter.
Ligresti was arrested along with her father and sister during a probe into false accounting at insurer Fondiaria-SAI, which her family controlled until last year.
Her father was placed under house arrest while she and her sister ended up behind bars.
Cancellieri had earlier admitted asking prison authorities to evaluate Ligresti's health.
The justice minister's critics accuse her fuelling cronyism and of acting out of a conflict of interest because of her long friendship with the family.
The opposition Five-star party said it would present a no-confidence motion against Cancellieri, with leader Beppe Grillo saying her aid "could appear to be seen as the payment of a debt".
Cancellieri's son, Piergiorgio Peluso, earned several million euros working as an executive at Fondiaria-SAI between 2011 and 2012.
The centre-right People of Freedom (PDL) party threw its support behind Cancellieri , while its strained coalition partner, the centre-left Democratic Party (PD), urged her to explain herself to parliament.