David Lee Simpson of Bath, N.Y., was infatuated with Arias and became upset by comments from the two female anchors, Maricopa County Sheriff Joe Arpaio said.
Investigators found guns, handcuffs and other items in Simpson's car after taking him into custody in Bath, Arpaio said.
The sheriff declined to name the two anchors because he says Turner Broadcasting, which owns CNN and HLN, had asked his agency not to publicly identify them. But he did say one works out of Atlanta and the other out of New York.
An indictment that charges Simpson, 48, with three counts of computer tampering and two counts of stalking had not yet been made publicly available late Monday afternoon.
Simpson also is accused of threatening a Phoenix woman who defended the anchors online.
Arpaio says Simpson quit his job last week at a Bath auto repair shop and was later pulled over by police as he was leaving town.
The sheriff said investigators don't know whether Simpson was intending to carry out his threats, but he said items found in Simpson's vehicle were disturbing. Authorities found several weapons, zip ties and a news clipping about last December's mass shooting in Newtown, Conn.
It wasn't immediately clear why Arpaio's office had jurisdiction to arrest Simpson in New York.
Simpson is expected to be brought to Arizona on Wednesday, Arpaio said. Court records show he does not yet have a lawyer.
Earlier this year, a Maricopa County jury convicted Arias of murder in the death of her boyfriend Travis Alexander, but the jury later deadlocked at the sentencing phase of her trial.
A new jury could be impaneled to decide sometime in late September whether Arias should be sentenced to death or life in prison.