The ad, created by BMB, centres on a husband and father who feels like an ogre because of the amount of time he spends at work, and the lack of time he spends with his family.
The man is shown as oversized, hunchbacked with teeth sticking out of his mouth and horns growing out of his head. When he goes on holiday with his family, he slowly loses his ogre looks and transforms back into his former self.
The Advertising Standards Authority (ASA) has received 80 complaints that the ad is offensive to people with facial and physical disfigurements, and that it trivialises disability.
The ASA said it has not yet decided whether to investigate the ad or not.
Thomson-owner TUI said in a statement: "We were sorry to hear that there were complaints to the ASA regarding our new "Simon the Ogre" advert.
"We’d like to re-assure customers that the aim of our advert was to bring to life the potential power of a holiday, and to portray a light-hearted view on a metaphor that might ring true for certain families – the idea of being busy with work and the stresses of life, and it then melting away once on holiday.
"We tested this advert with more than 28,000 customers and received an overwhelmingly positive response. There was never any intention to cause offence or disappointment.
Thomson said millions of people have now watched the ad and the majority of feedback has been "positive".