Tickets went on sale at 10am and by this afternoon the show - returning to London in May next year after an absence of more than a decade - had already passed £4.4 million at the box office.
The previous record was set in March when The Book Of Mormon took £2.1 million in a day.
Producer Sir Cameron Mackintosh said: "I'm truly flabbergasted with the box office take today.
"I knew people loved Miss Saigon and had taken it to their hearts but this is beyond my wildest dreams.
The atmosphere down at the theatre today is full of excitement and I can't wait to bring my new production back to the West End."
The show will begin its run at the Prince Edward Theatre on May 3 - 25 years after the production first opened in the West End - and tickets are being sold up to October 25 next year.
The epic musical by Alain Boublil and Claude-Michel Schonberg has been seen in 300 cities around the world and performed in 15 languages.