Officers were called to a residence in southwest Albuquerque around 1 a.m. Tuesday about a reported domestic disturbance.
They say a woman told them that her boyfriend was intoxicated and started arguing with her.
When she asked him to leave, he allegedly picked up her kitten that was sleeping in a box and violently threw the animal down against the floor.
Animal control officials arrived and took custody of the deceased kitten.
Police say 31-year-old Mason Hern is being held on a $5,000 cash or surety bond.
They didn't immediately know Tuesday if Hern has a lawyer yet.