The Scottish Government is proposing legislation to bring about a major expansion of electronic monitoring.
Changes could include introducing GPS and alcohol consumption monitoring technology.
Other possibilities are using tagging as a condition of a community payback order, during release from custody while a police investigation is ongoing or as a bail condition as an alternative to custody on remand. It could also give courts the option of using tagging instead of a fine.
Mr Matheson, who is also the Justice Secretary, said: “There will always be crimes where a prison sentence is the only reasonable response but international research backs our experience that prison is not always the most effective way to prevent repeat offending.
Electronic monitoring researcher Dr Hannah Graham, of Stirling University, added: “There’s a pressing need to reduce unnecessary and costly uses of prison in Scotland.
“International evidence shows electronic monitoring can be used effectively without routinely resorting to custody. This doesn’t mean indiscriminate tagging and surveillance en masse, nor does it mean ignoring victims. It means tailoring tagging to be fit-for-purpose, with due regard for all affected.”