The Apprentice host tweeted in December that a product from the brand Stylsmile would make a “perfect Xmas gift”.
He owns a 50% share in the business, which is run by a former winner of the reality show.
The advertising watchdog said the tweet breached guidelines and must not appear again.
“If you know someone who’s longing for whiter teeth, this is the perfect Xmas gift for them,” said Lord Sugar, 73, in the tweet, along with a link to the product’s website.
A complaint was raised about the post, questioning whether it was obvious it was an advert.
Lord Sugar and Stylsmile – run by inventor Tom Pellereau, who won the series in 2011 – argued that it was a well-known fact that Lord Sugar was a partner in the company, because it was made public on The Apprentice in front of millions of viewers.
They said Lord Sugar was known to post about his businesses on social media regularly, and the tweet was not a covert promotion.
However, the Advertising Standards Authority ruled that the tweet broke the advertising code. According to the rules, all advertising communications must be clearly marked, for example with the phrase “#ad” on social media posts.