The message, posted ahead of Farah's Olympic 5,000 metres final 12 days ago, was deleted shortly after it had been sent.
Farah, who added the 5,000 metres Olympic title to his 10,000 metres gold at London 2012, was born in Somalia but came to live in the United Kingdom, aged eight.
South Africa-born hooker Sharman, 25, publicly apologised for the tweet and closed his Twitter account.
In a statement, Premiership club Saints said: "Northampton Saints treats all such matters seriously.
"The club has a clear policy regarding social media and is following the procedures set out in that policy.
"Northampton Saints do not comment on individual cases."
Sharman has not been included in Northampton's match-day squads for either of their final two pre-season friendlies against Moseley and Edinburgh.
Northampton spokesman Chris Wearmouth told the Daily Telegraph website: "We have clear social media guidelines and we have regular meetings with the players over the use of Twitter throughout the year.
"They are reminded of their responsibilities and their place in Northampton society, playing for the biggest club in town.
"We are all aware that social media can have a positive effect. It's a great channel for fans to ask questions and players to answer them directly, but there are potential pitfalls.
"Fans expect our players to be role models.
"It can be very easy to tweet in the heat of the moment. Sometimes it's better to put the phone back in the pocket, think about it and tweet a more considered view later on."
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