The network said in a statement that Jarrett is "dealing with serious personal issues." A spokeswoman said Fox has not set a date for his return to work as a weekend co-anchor.
Jarrett, 59, of Larchmont, N.Y., was arrested early Wednesday afternoon after police responded to a call about a drunken man at the Northern Lights Grill, Patrick Hogan, a spokesman for Minneapolis-St. Paul International Airport, told the Minneapolis Star Tribune.
Jarrett was charged in Hennepin County District Court with a misdemeanor offense, obstructing the legal process, interfering with a police officer. He was given a June 6 court date.
A graduate of the University of California, Hastings College of Law, Jarrett covered the trial of George Zimmerman in Florida. He joined Fox in 2002 after a stint with MSNBC.
Fox said he has not appeared on air since April.