The pair had been dancing the rumba to 'Over The Rainbow' when Chmerkovskiy's leg appeared to give way, causing the couple to fall to the ground.
"To all the fans... I'm sorry! It will never happen again and I will never 'fall'! @kirstiealley You were... FLAWLESS! In more ways than one! (sic)" wrote Chmerkovskiy on his Twitter account.
In a message to Chmerkovskiy, Alley said: "I salute u... U r a gladiator .... A champion... I'm honoured to be your partner."
She later added to followers: "Thank u all for your support and your votes.... Sort of a beauty in Live TV... Because it's live... Anything can happen... gotta love it!!!! Maks is fine!!.. He's a pro... Dancers live through lots of pain... But thanks for your concern!!"
The pair eventually earned 21 out of 30 for the routine, with Carrie Ann Inaba, Bruno Tonioli and Len Goodman praising their ability to continue with the performance despite the mishap. Chmerkovskiy added to Brooke Burke backstage that the fall was likely because of muscle strain and had nothing to do with Alley.
Alley had dedicated her performance to her parents, explaining that her mother passed away following a car accident which nearly claimed the life of her father, after the pair were hit by a drunk driver.
Dancing with the Stars continues tonight on ABC.
> Click here for a full recap of this week's performances