The First Minister sought a student to work for free on constituency casework at his Inverurie office near Aberdeen.
But the voluntary post, advertised through Aberdeen University careers service, was condemned by political opponents and campaigners.
In an embarrassing move for Mr Salmond, the pressure group Intern Aware reported the advert to the taxman, requesting an inquiry into whether the role should pay the minimum wage.
The internship was advertised earlier this month and described as a "volunteering opportunity". However, the advert, featuring the SNP logo, detailed a list of high-level duties, including meeting constituents, dealing with local press, assisting staff with casework and administrative tasks.
The successful volunteer, who would receive travelling expenses, would require "excellent organisational skills", computer skills and an ability to write well, the ad stated.
The office has offered several internships in previous years, the advert said.
Intern Aware, which campaigns against "exploitative, exclusive and unfair" unpaid internships, called for an inquiry by the minimum wage unit of HM Revenue and Customs.
Under UK employment law, an intern would have to be paid if he or she is classed as a worker rather than a volunteer by the taxman.
Last year HMRC targeted 200 employers who had advertised internships to ensure they were paying the minimum wage where appropriate, amid growing concern over the spread of temporary work placements.
Chris Hares of Intern Aware said: "Unpaid internships exclude the vast majority of young people who can't afford to work for free.
"Senior politicians like Alex Salmond, who talk a good game on social mobility and young people, should know better than to ignore these principles in their own office.
"As well as being unfair, unpaid internships are often illegal. We will be reporting this advert for investigation by HMRC's Minimum Wage enforcement team."
Labour MSP Kez Dugdale said: "We face a real challenge in ensuring we have equality of opportunity for young people trying to make their way in the world and I strongly believe unpaid internships undermine that because they give an advantage to people from well-off backgrounds."
Sir Malcolm Bruce, the deputy leader of the Lib Dems, said: "If someone is doing the job of a paid worker then they need to be paid." He added: "It is hugely disappointing that the First Minister has failed to lead by example in his own constituency office."
The Scottish Labour leader Johann Lamont and Scots Lib Dem chief Willie Rennie have never hired unpaid interns, though both have offered work experience to school pupils in their offices. The Scots Tories are not opposed to unpaid internships, but a spokesman said leader Ruth Davidson had never recruited one.
A programme run by Edinburgh University has placed unpaid interns with MSPs on all sides, though the research work they do while at Holyrood is part of their academic course.
Last year the Government issued new guidance to young interns to ensure they were properly paid.
An SNP spokesman said: "We've simply responded to a request from Aberdeen University to provide a short-term flexible internship to one of their full-time students - to assist them with their course.
"No-one has been appointed, or even interviewed, and therefore there has been no discussion on expenses or hours for the internship."
A spokesman for the University of Aberdeen said: "We contacted Mr Salmond's office to see if they would be happy to participate in a work placement scheme organised through the University. The approach was made under our initiative, and in this case they offered a short-term voluntary placement which we then advertised to our students.
"These placement opportunities, whether voluntary or paid, can offer students relevant experience in the workplace in conjunction with their degree."
A spokesman for Mr Salmond's constituency office said: "All we are doing is providing a voluntary short-term placement as part of a university initiative to assist students with their studies.
"As Aberdeen University have made clear, it forms part of a university scheme, rendering any criticism both ridiculous and - in the case of that from other political parties - completely hypocritical."