It was reported earlier this week that King was rushed to A&E suffering from cellulitis after being bitten by a horse fly.
The disease - which causes inflammation of the skin - has since left her on crutches, forcing her to pull out of this Sunday's T4 On The Beach gig.
Bandmate Rochelle Wisemen tweeted: "Everyone please send [Mollie] some love, I really hope she gets well soon!! T4onthebeach isn't gonna be right without her :("
The event marks the first time the group will perform their new single 'Missing You'.