After a debate in the Scottish Parliament, MSPs backed a motion to encourage the use of community programmes and drug treatment services instead of jail sentences for female offenders.
Ms Jamieson's words came as she admitted Scotland's female prison population continued to rise year on year even though charities say women do not cope as well behind bars as male offenders.
Reforms would reflect the fact that most women's offending is very different from male crimes - often focusing more on theft and dishonesty than violence, she said.
Opening a debate in the Holyrood chamber, she said: "Most people agree that short-term prison sentences are neither the most appropriate nor the most effective way of challenging women's offending.
"I agree. It cannot be beyond us, working together, to radically reform how we manage women offenders in Scotland."
Official figures recently revealed a 13 per cent rise in the number of female prisoners, increasing from 297 in 2003 to 336 last year.
The minister said there were 313 women in prison in Scotland last week - very few of them for serious offences. About a third were either being held on remand or were serving sentences of under 12 months.
Dr Alison Elliot, Moderator of the General Assembly of the Church of Scotland, welcomed the debate.
She said: "Women's pattern of offending is quite different from that of men. Their circumstances on admission to prison are different, as is how they cope with imprisonment.
"If we can concentrate on how to deal with women in the criminal justice system, we will learn new things about how to relate imprisonment to rehabilitation, what alternatives to prison might be appropriate and how offenders can be reintegrated into society."
Frances Crook, the director of the Howard League for Penal Reform, said: "Women are being sent to prison in unacceptable numbers and are suffering disproportionately when they are inside. They are more prone to self harm."
© The Scotsman