Dogan Arslan, 47, is accused of staring at her and her Pollokshaws Road office from a parked car outside.
Arslan, from Battlefield, Glasgow, is alleged to have carried out the offence between October and December 2012.
It is alleged he engaged in conduct which caused people, including Ms Sturgeon "fear and alarm".
Arslan is said to have "repeatedly loitered within a parked motor vehicle in the vicinity of the office premises" and stared at the offices and Miss Sturgeon.
The case called at Glasgow Sheriff Court and was continued without plea until next month for a psychiatric assessment.
Arslan was arrested last year and appeared at the court on December 14, where he made no plea or declaration.