Lord Robertson, a former UK defence secretary in Tony Blair's government, spoke out against the dangers of "breaking up the solidarity of the West at this particular time".
In a speech in the US, he called on the people of Scotland to "properly and soberly examine the impact of their decision" in September's independence referendum on "the stability of the world".
Scotland's Deputy First Minister Nicola Sturgeon said she was "shocked" by Lord Robertson's "insulting and offensive" comments, adding that his language "does a real disservice" to the independence debate.
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 geopolitical terms.
"Nobody should underestimate the effect all of that would have on existing global balances, and the forces of darkness would simply love it."