Francis Rains, who lives in Kentucky, was called by a man who claimed she had won a lottery.
After first informing her of the imminent windfall, the mystery man then called back a few days later to ask for money.
He informed Ms Rains that she would need to pay off the taxes on the winnings before she would receive anything.
She also said that two other men, claiming to be FBI personnel and a lawyer, had called her to talk about the prize.
In an effort to prove his legitimacy, the caller sent Ms Rains a picture, which he claimed was of himself.
However, the photograph turned out to be a snap of Mr Alexander, the Liberal Democrat MP for Inverness, Nairn, Badenoch and Strathspey.
Ms Rains told her local radio station: "He [the caller] said I'd won $2.5m and a Mercedes-Benz.
"I sent some money. Being a dummy, but I sent it,"
Ms Rains refused to detail how much money she lost in the scam, although radio station WKYT initially claimed the total was in the "hundreds of dollars".
Mr Alexander said he was disgusted by the scam.
He added: "I deplore these scams and my heart goes out to the lady who has lost her money.
"I wish the US enforcement agencies well in bringing the perpetrators to justice."
Police said such scams are difficult to investigate because most calls come from outside the US.
In this instance, the fraudster is believed to have made the call from Jamaica.
Officials have warned never to send any money or give out any personal information, such as back account details, in similar situations.