MP Jack Dromey should not have used the potentially offensive word "Pikey" in a Twitter message but it was an "innocent mistake", Labour sources have said.
The shadow minister tweeted a picture of himself with a postal worker.
His caption said: "With Gareth Martin, the Pikey from the Erdington Royal Mail Sorting Office. A great guy!"
After he faced accusations of racism, Mr Dromey tweeted that Mr Martin's nickname was a reference to the Dad's Army character Pike.
Conservative MP David Morris has written to Metropolitan Police Commissioner Sir Bernard Hogan-Howe calling on him to investigate whether Mr Dromey's message constituted incitement to racial hatred.
"As I am sure that you are aware, the word 'pikey' is a deeply offensive word, and is a racially charged term due to its association with Irish travellers and Roma Gypsies," writes the Morecambe and Lunesdale MP.
"I have received a number of complaints from members of the travelling community in my constituency, and am writing on their behalf."
A Labour source said the party had spoken to Mr Dromey earlier on Friday after being contacted by journalists who had picked up on a growing Twitter storm about the comment.
"It was a stupid thing to do and he should not have said it," the source added, but he insisted it was "an innocent mistake".
He said the MP had been referring to the Dad's Army character rather than using a derogatory term for "somebody of Romany extraction".
Mr Dromey had agreed to issue a clarification after the potentially offensive nature of the tweet was pointed out to him.
The second message read: "Don't panic, Mr Mainwaring. This morning's meeting was with Gareth, a Postie nicknamed after Corporal Pike from Dad's Army."
Labour sources said the incident - not the first time Mr Dromey has landed himself in hot water over his use of social media - showed how important it was to think before tweeting, in case words were misconstrued.
"It is an offensive word and it just shows how everybody should be extremely careful with language on Twitter," said a spokesman.
Mr Dromey, a former trade union leader, is married to Labour's deputy leader and equalities spokeswoman Harriet Harman.
He is a shadow communities and local government minister and chairman of the all-party Parliamentary Group on Migration.