The First Minister spoke out after a Holyrood committee last week called for an end to the current ban on inmates voting which exists in Scotland to comply with the European Convention on human rights.(ECHR)
The SNP leader said she does want to see the most serious criminals, such as murderers and rapists, being enfranchised.
A report by Holyrood's Equalities and Human rights committee last week concluded that not being able to vote might impact negatively on an individual's rehabilitation and called for and to the ban.
Ms Sturgeon's scepticism was welcomed by Tory MSP Murdo Fraser who raised the issue at Holyrood.
Mr Fraser added: "All MSPs should be listening to the victims of crime like Mr Muir and standing up for their rights first."
The SNP leader insisted all MSPs will be mindful of crime victims.
She added; "I'm not making any criticism of the committee.
"The committee looked at this issue and have made recommendations as they're entitled to do. These are difficult and sensitive issues. We now have a power devolved to us that was previously reserved. Therefore we have an obligation to make sure that our laws in this country are compliant with the European Convention on Human Rights.
"But it is my view that we should not give the vote to all prisoners. I'm certainly not persuaded of enfranchising prisoners who are in prison for the most serious and heinous crimes and are perhaps in prison for lengthy periods of time."