LAPD officers arrested Molnar Thursday.
The L.A. District Attorney's Office on Monday declined to press charges due to lack of evidence, and Molnar was released from police custody.
Molnar allegedly stated: "The mayor knows who I am. The mayor is talking a lot of [expletive]. You tell him that I'm going to take him out."
In the declaration for the restraining-order request, Villaraigosa wrote: "I believe the threats uttered by Daniel John Molnar to be credible, and am concerned for the safety of the employees of my office, myself and my family when Daniel John Molnar is near."
The restraining order requires Molnar to stay at least 100 yards away from the mayor's home and from L.A. City Hall. Molnar is also prohibited from communicating with the mayor or his staff.
A police detective declared Molnar told police he thought the mayor was directly speaking to him through the television to threaten him.