Lord Wallace of Saltaire, who speaks for the Government on foreign affairs in the Lords, warned Britain's standing would be damaged.
The Liberal Democrat politician also said that losing Scotland could cut the UK's leverage just as it wants to renegotiate its relationship with the EU.
His judgment that independence would diminish the UK's influence in Europe was backed by other senior Conservative and Labour figures, including two MEPs.
The warning came as George Osborne told the European Union it must change if the UK is to remain a member.
Prime Minister David Cameron is expected to make a major speech on the UK's future relationship with Europe in The Hague in less than a fortnight.
The keenly anticipated speech is expected to call for a repatriation of powers from the EU.
Senior Tories have said the Prime Minister could face challenges to his leadership after the next election if he "fudges" the European issue.
But speaking at an event to mark 40 years of the UK's membership of the EU, Lord Wallace suggested any negotiation with Europe could be hampered by parallel talks over Scottish independence.
Asked if the UK would lose influence if Scotland broke away, he said "Yes, of course, we would be a smaller country".
He added: "Clearly it would damage Britain as a whole if Scotland were to leave – let alone the European dimension".
He also suggested the UK Government's treatment of Scotland during independence negotiations could limit its success in EU talks.
"These are going to be parallel processes," he said.
"One of the things that the unilateralists on the right wing of the London debate have to consider is if Alex Salmond really wants an 'a la carte' set of arrangements with England, where he can pick and choose which bits he would have and which bits would go, the English are going to resist. If at the same time we [the UK Government] are trying to do that deal with the EU, we will find these two processes difficult to manage.
"So we have got to recognise that how we treat the Scots, and how we assume our continuing relations with the EU, unavoidably overlap".
He said much the same was true for the Scottish Government, which he said could not adopt an "a la carte" approach to the EU.
He added that it was in Scotland's interests to stay in the EU, as it was for the rest of the UK.
Tory MP Andrea Leadsom agreed that the UK would lose influence if Scotland became independent as did Richard Ashworth MEP, Leader of the Conservatives in the European Parliament, and Mary Honeyball, the Labour MEP.
The administration of US President Barack Obama made clear it was keen to ensure the UK remains an integral part of the EU, while a senior German politician urged the UK not to "blackmail" Europe and suggested hopes of renegotiating a deal were all but impossible.
An SNP spokesman said: "It is the Tory/LibDem coalition that is threatening to rip the UK out of Europe, and the only guarantee of a strong Scottish voice in the EU is a Yes result in next year's referendum."
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