The Zoom call was reportedly an "election simulation", involving many of the magazine's biggest stars including Jane Mayer, Evan Osnos, Jelani Cobb and Sue Halpern.
Vice stated that Toobin was allegedly masturbating on the video call.
A CNN spokesperson said in a statement that "Jeff Toobin has asked for some time off while he deals with a personal issue, which we have granted".
The circumstances surrounding the incident are not completely clear however two people who were on the call have told Motherboard they witnessed Toobin masturbating, Daily Mail reported.
The pair, who did not give their names, said that the incident happened after a break in the call.
Toobin apparently seemed to be on a separate call and when the break was over could allegedly be seen touching his penis. Toobin then left the call before logging back in shortly afterwards seemingly unaware at what others had just witnessed.
It is also not clear how many staffers were on the video call at the time.
The 60-year-old Toobin has been a New Yorker writer for more than 20 years and joined CNN in 2002.
He is the author of several books, most recently True Crimes and Misdemeanors: The Investigation of Donald Trump, published in August.