The veteran backbencher, regarded as an expert on foreign affairs, also argued that the American government would not readily accept an independent Scotland into Nato if it kept to the Nationalist policy of ridding Scotland of the UK's nuclear arsenal as "quickly as possible", thought to mean within two years.
Sir Ming, a member of the Nato parliamentary assembly and in Washington this week as a member of the Commons Foreign Affairs Committee, was asked if the US - the key player in Nato - would readily accept an independent Scotland without nuclear weapons into the group.
He said: "No they won't. I have heard at private gatherings senior American officials make that point strongly."
He pointed out how it would be difficult for the US to exercise "some kind of veto" on an independent Scotland's application to become a member of Nato "but it could exercise a delay; it might say - you have to sit this out until we see what happens".
The MP for North East Fife, who announced recently he would stand down from the Commons at the 2015 General Election, warned that if an independent Scotland, under First Minister Alex Salmond, not only adopted a nuclear-free policy but also one which prohibited, say, nuclear submarines from Scottish waters, the nation could be ostracised by the Americans for a generation.
Sir Ming said: "Alex has gone out of his way to establish good relations with the US, Tartan Week and all that stuff. But that would count for nothing if the position adopted was such that Scotland was not going to be nuclear but also that American aircraft and ships would not be welcome."
In response, a Scottish Government source said Sir Ming's remarks were "well wide of the mark".
The source said: "An independent Scotland will have first-rate security arrangements to counter any threats we may face.
"And we will continue to work in close co-operation with the rest of the UK and international partners on security and intelligence matters, which is in everyone's interests.
"We have made clear that an independent Scotland's membership of Nato is contingent on this country not hosting nuclear weapons; something that will put us in the same category as the overwhelming majority of members of the alliance."