The One Direction star was invited to the actor's studio with the rest of the band while in the US, but was afraid he would be too starstruck if he came face to face with the Pirates of the Caribbean star.
"I was too nervous to go. I am a massive, massive fan and I didn't want to embarrass myself so I let the boys go without me," Malik told The Sun.
"Hopefully, there will be a next time. The boys said he was totally cool. I kind of regret it for sure and the lads said I was a scaredy cat."
He added: "Some of our fans get so excited or nervous when they meet us and that's how I was at the thought of being with Johnny. But instead of lapping it up and enjoying it, I ran the other way."
The rest of the boys visited Depp and performed a few songs for his daughter Lily-Rose.
Malik was recently involved in a Twitter feud with The Wanted, branding Max George "chlamydia boy".
Watch One Direction's video for 'Little Things' below: