A spectator who attended Saturday's match at Twickenham said in a letter published by British newspaper The Guardian that a "bunch of men" hurled "nasty, foul-mouthed, racist, homophobic abuse" at Owens, who is gay.
The RFU says "we take any allegations of any abuse very seriously and are investigating this matter."
Owens, who is from Wales, is widely regarded as one of rugby's top referees.