Lord Sugar was made the focus of a police investigation after posting an allegedly racist tweet that makes light of child labour in Asia.
The 66-year-old entrepreneur posted a photo of a young Chinese boy crying. In the caption, he said the boy was upset after being told off for leaving the production line of Apple's iPhone 5.
In 2010, Apple admitted to using child labour in three of its factories where its products are assembled - mainly in China. The company said it was no longer using these factories in a statement.
Apple has been criticised repeatedly for using factories that offer poor working conditions.
"The kid in the middle is upset because he was told off for leaving the production line of the iPhone," Lord Sugar said. His tweet was reposted over 400 times.
According to the Mail on Sunday, the Metropolitan Police received a complaint about the tweet and, after the complainant made a statement, officers from Merseyside's Hate Crime Investigation Unit looked into whether a crime had been committed.
The officers eventually classed the remark as a "hate incident", meaning no further action will be taken, but details of the event will be kept on file.
Nichola Szeto, who reported the tweet and whose husband and family are Chinese, said: "I thought racism was illegal."
Lord Sugar has not commented on the investigation and he has not removed the tweet from his account. He had also posted the same picture with the caption "Mrs Beckham new range of kiddie wear".
The complaint was condemned by Matthew Sinclair, chief executive of the TaxPayers' Alliance, who said: "Individuals must be held to account for their actions, even on social media, but officers should not waste their time chasing every ill-thought-out tweet."