Dr Steve Forman, who has played with David Bowie and Pink Floyd, could not extend his visa due to salary restrictions.
Dr Forman has taught at the Royal Conservatoire of Scotland (RCS) in Glasgow for four years.
He is currently appealing against the Home Office decision.
The UK government website states that the "appropriate salary rate" for an experienced higher education teaching professional who wishes a visa to remain in the UK is Â£31,200.
Dr Forman said he could not meet this minimum salary requirements for a Tier 2 visa.
He therefore applied for leave outside of the rules under Article 8 of the European Convention of Human Rights, which states that everyone has the right to respect for their private and family life.
The Home Office said that Dr Forman could not demonstrate the requirements needed to stay in the UK.
Dr Forman's film score credits include ET and Pretty Woman and he has recorded with The Beach Boys, David Bowie and Fleetwood Mac.
He said: "I would like to see the UK Border Agency look at the value gained and the value lost from me leaving Scotland when I am contributing full-time to society on many different levels.
"I am in the community playing traditional music with some of the finest musicians I have ever heard. I would like to stay involved with life and I would like to do this in Scotland where I live, where my friends are and where my family is."
A change.org petition for the reinstatement of Steve Forman's work visa has attracted nearly 1,500 signatures since it was started on Tuesday morning.
He has been in the UK for more than seven years and has taught at the Royal Conservatoire of Scotland (RCS) for four years. His position there has been suspended pending confirmation of his status.
A Scottish government spokesman said: "The talent and expertise of people such as Steve Forman make a welcome contribution to developing Scotland's future musical talent. The Scottish government is aware of Mr Forman's situation and we are liaising with the Home Office on this case.
"This case reinforces existing Scottish government concerns that immigration policy in the UK is inflexible and does not address Scotland's particular economic and demographic needs."
Dr Forman's solicitor Fraser Latta described the case as "truly exceptional" and said that the Home Office had "clearly failed to give proper consideration to his individual rights and the rights of the community which he is a valued member of".
He said it was indicative of the current immigration system where a talented and respected person can be disregarded rather than cherished.
A spokesperson for RCS said: "Steve Forman will be sorely missed by staff and the students. He is a well-respected teacher and an expert in his area.
"We have been very supportive of Steve. We have done our utmost to support him through this for some time now. The UK Border Agency made a decision on his eligibility to stay in the UK and we have to abide by that."
A Home Office spokesperson said: "All visa applications are considered on their individual merits and in line with the immigration rules.
"Dr Forman's application was refused because he could not demonstrate he met the requirements for leave to remain in the UK. He has appealed this decision and it would therefore be inappropriate to comment further at this stage."

Kante, 24, and Benalouane, 28, have both penned four-year deals and are the first signings by Claudio Ranieri.
The French midfielder helped Caen win promotion in 2013-14 and played 37 times in France's top flight last term.
Centre-back Benalouane is a former France Under-21 international but has opted to represent Tunisia.
Benalouane's move is subject to international clearance as well as Premier League and FA approval.
The double signing adds to new arrivals Robert Huth, Christian Fuchs and Shinji Okazaki at the Foxes, who finished 14th in the Premier League last season.
Leicester begin their Premier League season against Sunderland on Saturday.
Find all the latest football transfers on our dedicated page.
The Scottish government has called on the Home Office to reconsider the case of an American percussionist who is at risk of being deported from Scotland.
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Leicester City have signed Yohan Benalouane from Italian side Atalanta and N'Golo Kante from French club Caen for undisclosed fees.