The music event at Wembley Stadium would have been Malik's first live UK solo stage performance.
In a message on his Instagram account on Saturday, the former One Direction star apologised "to everybody I've let down" and explained that his anxiety about performing live "has gotten the better of me".
He said: "To all those people who have been waiting to see me perform at the Capital Summertime Ball today.
"I flew into the UK last night to appear in my home country in front of my family, friends, and most importantly my UK fans.
"Unfortunately my anxiety that has haunted me throughout the last few months around live performances has gotten the better of me ... with the magnitude of the event, I have suffered the worst anxiety of my career."
The 23-year-old added: " I cannot apologise enough, but I want to be honest with everyone who has patiently waited to see me.
"I promise I will do my best to make this up to everybody I've let down today.