Swarthick Salins' savings were below the level required by the Home Office
First Minister Alex Salmond has written to Home Secretary Jacqui Smith urging her to reverse an immigration tribunal decision.
Swarthick Salins has been told he will be deported with his family because his savings were £78 less than the £800 specified by Home Office rules.
Mr Salins, a 37-year-old Indian, has lived in Scotland for nine years and his three children were born in the UK.
Mr Salmond said the decision was "overly harsh".
In his letter to Ms Smith, Mr Salmond said: "I am disappointed to hear that Mr Salins has been denied leave to remain after his bank balance fell below the £800 maintenance requirement by £80.
"On the face of it this decision appears to have been overly harsh, and I would greatly appreciate you reviewing the case and sharing the detail and the reasoning behind the decision with me."
He said that in a time of a declining population, Scotland needed to "attract and retain bright, talented individuals who can make a contribution to our economic prosperity and our communities, such as Mr Salins and his family".
He pointed out that Mr Salins' children, who live with him in Perth, had known no other home.
"Clearly, we need to inspire confidence in the fairness of the new Points Based System of Managed Migration," he said.
"I hope therefore that you are able to intervene in this case to rectify what appears to have been an overly harsh interpretation of the legislation."
Mr Salins did a PhD at St Andrews University with backing from a charity set up by Scotland's richest woman, bus tycoon Ann Gloag.
He is s planning to lodge an appeal against the decision at the Court of Session in Edinburgh.
Last week, a UK Border Agency spokesman said: "It is important that migrants are able to support themselves and their dependants when they are here.
"Allowing the entry of those unable to support themselves would have negative social consequences for the individual and for the UK."