The figure-hugging Jean Louis gown, with 2,500 crystals, was bought by the Ripley's Believe It or Not museum chain, exceeding the USD 3 million guide price.
The company's vice president said it was "most iconic piece of pop culture that there is", reported BBC.
Monroe died from a drug overdose just three months after the performance.
The sultry rendition for President Kennedy's 45th birthday at a 1962 Democratic fundraiser at New York's Madison Square was one of her last public appearances. President Kennedy was shot dead a year later.
More From This Section
The sum raised is likely to set a new world record for the most expensive dress sold at auction.
Monroe's billowing white dress from "The Seven Year Itch" sold for USD 4.6 million in 2011.
The largest collection of the screen star's possessions ever offered for auction is being sold by Julien's auction house in Beverly Hills over three days.
Also sold on Thursday was the cocktail dress she wore in "Some Like it Hot", which fetched USD 450,000.
She bequeathed her personal effects and clothing to him in her will.