A Texas vet who shot a domestic cat through the head with a bow and arrow before posing with the dead animal on Facebook has been sacked as police launched an investigation into the slaying.

Kristen Lindsey triggered an avalanche of complaints and several online death threats after posting a picture of herself smiling with the assassinated ginger and white adult male.

"My first bow kill, lol. The only good feral tomcat is one with an arrow through it's head! Vet of the year award ... Gladly accepted," read a caption accompanying the post, which was later deleted and Lindsey's Facebook account was taken offline amid the outcry.

Local media said the cat belonged to an elderly couple who had reported it missing.

Lindsey's employer, the Washington Animal Clinic, confirmed she had been sacked.

The Austin County Sheriff's department appealed for outraged members of the public to take it easy on inundated switchboard operators.