International development minister Alasdair Allan claimed Brexit will cause "immeasurable harm" to Scotland.
He said further damage could be inflicted by limiting the number of people who can come to the UK.
The UK government said the immigration system takes Scotland's needs into account.
The Scottish government has vowed to oppose any changes to the rules which create barriers for businesses by preventing them from taking on the staff they need.
The number of people living in Scotland is projected to grow by 7% between 2014 and 2039, with 90% of the rise in the next decade expected to come from inward migration.
In a letter to the UK Home Affairs Select Committee's inquiry into immigration policy, Mr Allan said a "key priority" in tackling Scotland's ageing population was attracting working-age migrants to the country.
He said: "That is why we need the UK government to deliver an immigration system that meets Scotland's needs - because we depend heavily on new Scots to support our economy and communities.
"However, net migration targets and caps are too blunt an instrument to address the complex needs of our economy.
"The UK government's focus on arbitrarily reducing net migration figures, irrespective of the value migrants bring, what skills shortages they could address or what contribution they could make, is wrong for Scotland and is harming our economic prospects."
The UK government has already rejected a call to consider devolving immigration powers to Scotland and changing visa arrangements to encourage students from other countries to stay on north of the border after graduating.
A Scottish Affairs Committee report recommended UK ministers consider "sub-national migration powers" for Scotland and a tailored post-study work scheme.
The UK government response, published on Friday, stated it "does not intend to reintroduce a general post-study work scheme for Scotland" and stressed the immigration system is "designed for the whole of the UK" but takes Scotland's needs into account.
Any moves by the UK government to limit immigration could "seriously harm" Scotland's economy, a Holyrood minister has warned.