The 36-year-old Czech national was arrested on Saturday.
Pupils Back At School Following Bailey Gwynne Stabbing
Pupils are returning for the first time since a 16-year-old was stabbed.
Nicola Sturgeon is in the city for a private meeting with police and council officials after Bailey Gwynne's death last week.
Fifth-year pupil Bailey died on Wednesday after an incident at Cults Academy.
This morning, the comprehensive school opened for the first time since his death, with more than 1,000 pupils going back to classes.
Ms Sturgeon said: ''My thoughts remain with Bailey's loved ones and, indeed, all of those who knew him following this heartbreaking incident.''
The First Minister spoke ahead of private talks with Chief Superintendent Adrian Watson, Police Scotland's commander in Aberdeen, city council leader Jenny Laing and chief executive Angela Scott.
Ms Sturgeon stated: ''Everyone in Scotland was deeply shocked and saddened by the events last week, and it is important for me to let the council and the police know, in person, that the Scottish Government stands ready to provide any help that may be needed as they support the school community in the weeks and months ahead.
''Bailey will never be forgotten but as the students return to Cults Academy today, I hope that they can begin to see a semblance of normality and begin the healing process.
''The response to this tragedy - from everyone in Aberdeen - has been truly remarkable and I hope that the community spirit and support we have seen can offer a small amount of light in the city at this difficult time.''
Council leaders have already said measures have been put in place to help pupils, families and staff affected on their return.
Floral tributes have been moved from the gates of the school to a private courtyard where pupils can pay their respects and special assemblies are due to be held.
Hundreds of the dead pupil's friends and fellow students attended a vigil at Cults Parish Church on Thursday night, where candles were lit and messages of condolence written.
A 16-year-old boy, who cannot be named for legal reasons, has been charged with murder and remanded in custody.
He was also charged with having a blade or point on school premises and is expected to appear in court again on November 6.
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The Scottish Government has appointed an independent adviser to spearhead efforts to tackle racism.
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