She said, if the party was re-elected in May's Scottish Parliament election, it would introduce a more "progressive" local tax from April 2017.
The reforms could see councils given a share of income tax revenues in an effort to give them an "incentive" to boost economic growth.
Last year, a commission on reform called for a "more progressive" tax.
The Commission on Local Tax Reform did not recommend a single alternative but it suggested there could be merit in combining a property-based levy with an element of income tax.
The current council tax charges householders on the value of the property they live in. The rate it is charged at has been frozen by the Scottish government since 2007.
Speaking at the David Hume Institute in Edinburgh, Ms Sturgeon said: "The report from the cross-party Commission on Local Tax Reform made clear that now is the time to reform local taxation.
"The commission argued for measures which will make council tax more progressive, and which will give greater assistance to people on lower incomes.
"So next week we will set out details of how we intend to achieve this from April 2017 onwards.
"These changes will be part of a longer term plan to increase the accountability of local councils to the populations they serve."
Discussions with local authorities are expected to determine how the Scottish Parliament can gain more power over income tax and local authorities can secure a share of income tax revenues for their area.
Asked if councils should be given power over sales and tourism taxes, as recommended by the commission, Ms Sturgeon said priority would be given to the assignation of income tax and other council tax powers would be considered.
"Scotland is a small country and I think it is right that we take steps to incentivise local authorities to boost economic growth in their own areas, but equally I think we have got to be careful about creating a postcode lottery in terms of tax rates in different local authority areas."
The SNP will set out details of its plans on council tax reform next week, First Minister Nicola Sturgeon said.