F&C, which runs money from Edinburgh, London and Amsterdam, concluded the drive to find oil and gas off Greenland is too risky on both environmental and safety grounds.
Cairn has already faced objections from green activists worried that harsh conditions in the region could lead to an oil spill and hamper any clean-up in what they say is a fragile environment.
Karina Litvack, director of governance and sustainable investment at F&C, said: "Cairn Energy has been removed from our Stewardship range of funds because of its move into Arctic drilling.
"We feel that the level of environmental and safety management and the levels of oversight by the Greenland Government is not sufficient to give us comfort."
F&C said Cairn was not singled out as a company but was excluded from its 2.6 billion dollar Stewardship range of funds after it adopted a general policy to screen out any oil firm drilling in the Arctic.
F&C, which retains holdings in Cairn in other funds, previously crossed swords with the company earlier this year when it was among a group of investors that forced it to drop plans to give company founder Sir Bill Gammell a £2.5 million bonus.
Edinburgh consultant Wood Mackenzie estimates that one-fifth of the world's undiscovered oil reserves, or 20 billion barrels, might be located in Greenland's waters.
Cairn has spent 1.2bn dollar (£757m) drilling eight exploration wells to the south and west of Greenland.
However, it has not yet made any major discoveries and has no plans to drill in the region this year.
Francis Stuart, policy officer at Friends of the Earth Scotland, said: "This decision by F&C shows that even some of the most mainstream investors are seeing Cairn's activities as economically risky and environmentally irresponsible."
A spokesman for Cairn said: "Wherever it is active, Cairn seeks to operate in a safe and prudent manner. The Greenland Bureau of Minerals and Petroleum has established some of the most stringent operating regulations anywhere globally."
Meanwhile, F&C is also preparing to tackle British banks over their pay levels.
The company voted against pay reports from banks HSBC, Barclays and Lloyds last year, although it backed Royal Bank of Scotland.
Ms Litvak said: "The bank sector has to regain the trust of the public and its investors."
She added: "Still today there is a hankering to go back to the old ways and we see it right now with a lot of the push-back we see from banks on pay."