Police investigated Lord Sugar after a woman claimed a tweet he sent was racist.
The tycoon posted a photo of a Chinese boy wearing shorts made from watermelons, which went viral on China's equivalent of Twitter in August.
In a reference to one of the pictures showing the boy crying, Sugar joked: "The kid in the middle is upset because he was told off for leaving the production line of the iPhone 5."
The kid in the middle is upset because he was told off for leaving the production line of the iPhone 5 pic.twitter.com/DYCM9GfgM5
— Lord Sugar (@Lord_Sugar) September 30, 2013
Shop owner Nichola Szeto, from Liverpool, was offended by the reference to the Asian factories where the mobiles are produced and sent a complaint about the "racist tweets" to the Metropolitan Police.
She was then contacted by Merseyside Police and went to a Liverpool police station to make a statement.
Lord Sugar's message was investigated by the force's specialist hate crime investigation team, who decided that it should be classed as a "hate incident" although no crime had taken place.
On Sunday, after the Mail on Sunday reported the story, Szeto posted a statement on Twitter.
She said she had not phoned the police, but did complain online, and confirmed she had visited the police station to make a statement because "I wanted to just voice my opinion and be heard".
Her statement went on:
I am of mixed English/Chinese heritage & my partner & children are chinese. What you wrote did offend me. I am not sorry for voicing my opinion because you would have done exactly the same if you were me.
She admitted she had probably over-reacted, but added: "I have no doubt that you would have felt exactly the same way, had you been in my shoes."
A police spokesman said: "Merseyside Police can confirm officers received a complaint in relation to the tweet sent on the evening of Sunday September 30.
"The communication has been examined by the force's specialist hate crime investigation team and at this time it has been recorded as a hate incident and no criminal offences have taken place.
"Officers from the specialist team will be contacting the person who made the initial complaint to discuss this."