The former shadow Scottish Secretary, speaking in America, said a "debilitating divorce" after the vote in September would threaten the stability of the wider world.
He said he believed the American administration was worried about the possibility of Scottish independence and urged the US to make its views public, along with all British allies.
In a powerful speech at the Brookings Institute, Lord Robertson said: "The loudest cheers for the break-up of Britain would be from our adversaries and from our enemies.
"For the second military power in the west to shatter this year would be cataclysmic in geo-political terms.
"This is not a purely domestic matter even though it's a decision that will be taken by the Scottish people.
"The Scottish people need to be conscious that they are taking a decision, not just for themselves and for future generations in a one-off vote, but that it also has an effect elsewhere and people who are affected, or think they will be affected, have every right to speak out."
The Scottish government said the comments were "crass and offensive".
A spokesman for First Minister Alex Salmond said: "Scotland can and will make a hugely positive contribution to the world as an independent country - and our referendum is a model of democracy, which was cited as such only last month by the US Secretary of State.
"It is disappointing but not surprising that Lord Robertson fails to recognise any of that in this crass and offensive speech that has absolutely nothing positive to say.
"And it is contributions like his which are turning people across Scotland in their droves away from the fear and smear tactics of the No campaign towards the positive, upbeat, optimistic message of the Yes campaign.
"Lord Robertson once claimed having a Scottish Parliament would kill demand for independence stone dead - with comments like this it is the No campaign that will continue to sink like a stone."
Deputy First Minister Nicola Sturgeon said she was "shocked" by the language of the former Labour defence secretary.
Ms Sturgeon said: "Lord Robertson is a long-standing and very vociferous opponent of independence, so on one level I perhaps shouldn't be too surprised by the comments that he's made.
"On another level though, I am quite shocked at these comments. The contribution George Robertson made last night, and in particular the language he's used to make it in, I think does a real disservice to the debate.
"Look at some of the language: 'It would be cataclysmic for Scotland to become independent, it would aid the forces of darkness, it would threaten the stability of the western world'. That just completely moves away from any semblance of rational debate and I think many people, whether they're Yes or No, will find these comments insulting and offensive."
But Lord Robertson responded that he wanted other countries to speak out about the impact Scotland leaving the UK could have.
"I want all those in the world who understand that the break-up of the United Kingdom would have cataclysmic geo-strategic effects, breaking up the solidarity of the West at this particular time, to say that," he said.
"If people are worried about it, and I know they are, then I would hope that they would give the message that they would like the United Kingdom to stay together."
He said Scottish Government plans to remove Trident nuclear submarines from their base on the Clyde in Scotland in the event of independence could make it "very difficult for Nato to accept them" as a member.
"Effectively, they wouldn't just be disarming an independent Scotland, they would effectively be disarming the remainder of the United Kingdom," Lord Robertson said
"I don't think that that would be viewed with great comfort or with any great satisfaction by those in the alliance who believe that Britain's nuclear deterrent is part and parcel of the West's security."
He also insisted he was not scaremongering, saying: "I think if people think carefully about the world as it is today and what we've seen in Ukraine, what we see in Syria, what we see in the East China Sea and elsewhere, they'll recognise that this is a time for solidarity and solidity among the countries that are known as the West and the break-up of one of the principal countries in the West would certainly have major repercussions in the world, and people in Scotland I know will bear that in mind."