A picture Mr Zuckerberg's sister posted on her personal Facebook profile was seen by a marketing director, who then posted the picture to Twitter and her more than 40,000 followers.
That did not sit well with Randi, who tweeted to Callie Schweitzer that the picture was meant for friends only.
Ms Schweitzer replied by saying the picture popped up on her Facebook news feed.
Ms Zuckerberg eventually said Ms Schweitzer was able to see the picture because they had a mutual friend. Those tweets have since been taken down.
Many people reacted sharply to Ms Zuckerberg, saying that her brother's company makes privacy settings hard to navigate.