He made a gag in a video teasing his artificial intelligence app, Jarvis, which is voiced by Morgan Freeman.
When the Facebook founder says "play some good Nickelback songs" Jarvis replies "I'm sorry Mark, I'm afraid I can't do that - there are no good Nickelback songs".
"Good. That was actually a test," Zuckerberg responds.
The singer, who is married to the band's frontman Chad Kroeger, took offence at the joke and got in touch with Facebook.
"Many people use your products - some people love them and some people don't," she wrote.
