The Apprentice presenter took down the post after being accused of racism, writing: "Seems it has been interpreted in the wrong way as offensive by a few people... frankly I can't see that but I think it's funny."
Alongside the picture of the Senegal team, Sugar also posted images of sunglasses and handbags for sale on a beach.
Actress Kelechi Okafor tweeted that Sugar was "constructing this joke on the premise that all black people look alike, are poor and cannot achieve social mobility.
"This is why I say that racism is too deeply ingrained within the British psyche for certain people to even realise how damaging and hurtful their 'jokes' are."
BBC journalist Babita Sharma added: "A shocking, vile tweet that you take a screen grab of because you know it will soon be deleted."
Sugar responded: "If it so vile why have you retweeted it. You make me sick."
Sugar made his fortune as founder of electronics company Amstrad, and is estimated to be worth £1.15 billion ($1.5 billion, 1.3 billion euros).
He was chairman of Premier League club Tottenham between 1991 and 2001, and has presented the British version of The Apprentice since 2005.
Labour prime minister Gordon Brown made Sugar, 71, a lord in 2009, but he left the party in 2015, citing its "negative business policies".
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