South African hooker Brett Sharman tweeted "Good luck Mohammed running for Paki... I mean Great Britain..." as the Somalian-born runner was gearing up for his 5,000m run.
Sharman, 25, has since apologised for his tweet and deleted his Twitter account, but his club side have decided to conduct an internal investigation into the matter.
"Northampton Saints treats all such matters seriously," said a club spokesman.
"The club has a clear policy regarding social media and is following the procedures set out in that policy.
"Northampton Saints does not comment on individual cases."
Sharman joined the Saints in 2008, regularly filling in for Dylan Hartley while the Englishman is away on international duty.