Under the plans – which the Government is seeking to speed through Holyrood – between 260 and 390 prisoners could be released by early February in three tranches over six weeks.
Prisoners who have been convicted of sexual or domestic violence offences will not be allowed early release under the plans.
The Scottish Government estimates the change, which would apply to all prisoners, including those sentenced after the change comes into effect, will reduce the prison population by around 5%.
The Prisoners (Early Release) (Scotland) Bill – which was lodged in Holyrood on Monday – would also make small changes to how ministers can alter the automatic early release points for prisoners.
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On Tuesday, Ms Constance said: “The prison population has continued to rise and is projected to reach critical levels again.
“Long-term action is necessary to deliver a sustained reduction to the prison population and support the effective functioning of prisons.
“The proposals include built-in exemptions for those serving sentences for sexual offences or domestic abuse.
“We need the prison system to focus on those who pose the greatest risk to the public and provide a range of support to help reduce reoffending and integration back into the community.
“I very much recognise the concerns that may arise from victims and their families.
“The confidence of victims and the safety of communities is vital, and I will engage with victims’ organisations ahead of any changes.”
A spokesman for the Scottish Prison Service said: “We continue to manage an extremely high and complex population, with many of our establishments full beyond their design capacity.
“This restricts our staff’s ability to do the quality work that supports people’s rehabilitative journeys, prepares them for release, reduces the risk of reoffending, and helps build safer communities.
“We welcome the launch of this Bill and the focus it places on addressing the challenges we face.”
