The X Factor winner joined the production as part of BBC Children in Need's Pop Goes the Musical programme.
"That was amazing!" Burke said. "I'm so excited to be part of BBC Children in Need this year.
"It's an amazing cause and helps so many people. I was absolutely blown away by Les Misérables when I saw the show and to join the cast of one of the West End's most famous musicals was a real honour."
She added on Twitter: "I don't say this often. But I'm so proud. So proud to be a part of this for Children in Need & raising money for a great cause.
"Giving back means so much2me & to do this with @lesmisofficial has made me happy girl. Such an honour a moment I will never forget."
Burke continued: "Thank you so much to those who supported me. I'm left speechless with how proud I am of this moment. Thank you @lesmisofficial and@BBCCiN x Last night really did happen :) ... So happy.... "
Bookings are now being taken for other events in the Pop Goes the Musical series.
Blue feature in Jersey Boys on October 11 and Geri Halliwell appears in Singin' in the Rain on October 25. Thriller Live features Macy Gray and Stooshe for November 15.
Tickets are available via lastminute.com and are priced at £80.
Tickets include a top-price seat, signed programme, Pudsey bear, complimentary drink and VIP area access.
Watch the Alexandra Burke 'Let It Go' music video below: