Alvarez, 28, allegedly was involved in a fight with her husband Thursday.
She was arrested on suspicion of battery against a member of a household, officials said.
She was booked into the Doña Ana County Detention Center. She was released on a $1,000 bond later that day.
Alvarez is a news anchor for El Paso NBC affiliate KTSM.
“We are aware of the arrest but will wait for more details before making any other comments,” said Gary Sotir, general manager of KTSM/KDBC.