Celebrity Dog Tika the Iggy Dead at 14

11/5 12:03 PM PT -- Tika’s owner Thomas Shapiro tells TMZ ... "Tika had just wrapped what would be her final Fashion Week and PetCon appearances, and the family had planned to retire her so she could enjoy her relaxed final year at home.  Even though they had consulted with some of the best medicical professionals in the country, it was her time to go."

Tika the Iggy, an Italian greyhound with a fashion sense and a huge internet following, is dead.

Tika's owner, Thomas Shapiro, announced her death Tuesday in a heartbreaking social media post.

Shapiro says Tika had two tumors in her liver and they had surgery to remove them -- on the advice of veterinarians -- and things seemed like they were going well.

The surgery was a success, Shapiro says, and Tika was discharged from a clinic without complications ... and on her first night home, she had her favorite food, chicken, and everything appeared on the up and up.

But Shapiro says Tika was totally different on the second day after surgery ... looking tired and not quite herself, but peaceful. He says vets believed it was just a side effect from pain killers, but he says they soon found out her body was "slowly giving up."

Shapiro says Tika spent her final moments at home with her humans.

Tika had over 1.6 million Instagram followers and she was famous for showing off her fashionable outfits ... being hailed by some as "a new fashion it girl" and "the Anna Wintour of dogs."

Tika was 14.