The off-the-shoulder bodiced Victor Edelstein frock, which flares up at the knee, is one of the most recognisable dresses ever worn by Diana, who died in 1997.
The dress, offered as part of a "Passion for Fashion" sale by Kerry Taylor Auctions in London, had an estimated price tag of 250,000-300,000 pounds ($320,750 - $385,000). However it failed to reach those figures during live bidding.
Before the sale, auctioneer Kerry Taylor told Reuters there had been buyer interest from Britain and the United States. She said the dress had previously been bought in 2013 for 200,000 pounds "by a romantic gentleman who wanted basically to cheer up his wife".
"But since then it's spent most of its time locked away in a wardrobe and now as a couple they feel they really want this to go out into the public domain."
In an interview with Yahoo Entertainment last week, Travolta said he was nervous when he and Diana took to floor.
"(I thought) I’ve got to go back to my school days of learning ballroom dancing and show that I can lead her," the "Grease" and "Saturday Night Fever" star said.
"I didn't know until I got there that I was supposed to dance with her ... (Diana) didn’t know that (then U.S. First Lady) Nancy Reagan hadn't told me yet that this was the plan, that I was the Prince Charming of the evening."
The two Diana dresses that sold were a Katherine Cusack midnight blue velvet evening gown, which went for a hammer price of 48,000 pounds - above its 20,000 - 30,000 pounds estimate - and a short navy Catherine Walker day outfit, which had a 4,000 - 6,000 pound price tag and went for 28,000 pounds.
Other items under the hammer included pieces by Givenchy, Christian Dior and other luxury labels.
A Gabrielle Chanel embroidered evening coat, dating from 1918-20, sold for 90,000 pounds - well above its 8,000 - 12,000 pound estimate. An Autumn-Winter 1967-68 Balenciaga cocktail dress sold for 18,000 pounds.
A rare ensemble by designer John Galliano - entitled "Afghanistan Repudiates Western Ideals" and made up of a tail-coat with exaggerated shoulders, an oversized striped cotton shirt and loose dhoti trousers - sold for 70,000 pounds.