The 32-year-old Canadian singer accused Zuckerberg of "promoting bullying" in a post Thursday after the Facebook founder poked fun at Nickelback, her estranged husband Chad Kroeger's band.
"Dear Mark," Lavigne wrote. "Many people use your products - some people love them and some people don't. Either way, you're allowed your musical opinion however, your jab at Nickelback is in poor taste."
"When you have a voice like yours, you may want to consider being more responsible with promoting bullying, especially given what's going on in the world today," she added. "#SayNoToBullying #TheJokeIsOld #NickelbackHasSoldOver50MillionAlbums."
Zuckerberg had dissed Nickelback in a video introducing his home AI assistant, Jarvis, this week. He asked Jarvis to play "some good Nickelback songs" in the promo, prompting a less-than-flattering response.
"I'm sorry, Mark. I'm afraid I can't do that. There are no good Nickelback songs," the program answers.
"Good! That was actually a test," the Facebook founder says. "How about just play some songs that our whole family likes?"
Lavigne and Kroeger announced their separation in September 2015 after two years of marriage. The couple sparked reconciliation rumors in March after they reunited in the studio, and attended the Juno Awards together the next month.
"It is with a heavy heart that Chad and I announce our separation today," Lavigne said at the time of their split. "We are still, and forever will be, the best of friends, and will always care deeply for each other."