Former shadow minister Helen Goodman had tweeted: "If China is so great, why did @Jeremy_Hunt's wife come to England?" She has since deleted it.
It comes after Mr Hunt said the UK had to become as hard working as Asia.
The Labour Party said the tweet did not represent its views and that the Bishop Auckland MP would be reminded of her responsibilities.
Issuing an apology on Twitter, Ms Goodman wrote: "Wish to absolutely totally apologise for earlier tweet."
Several other MPs had replied to her original message, with former Communities and Local Government Secretary Eric Pickles saying he was surprised she could "send out something so vile".
Fellow Conservative MP Nadhim Zahawi even asked if Ms Goodman's account had been hacked, writing: "Helen that is a terrible thing so say. I hope you delete and apologise to Mrs Hunt."
And Lib Dem leader Tim Farron wrote: "Clearly she missed the 'kinder politics' memo", pointing to Labour leader Jeremy Corbyn's call for an end to personal attacks in politics.
Mr Hunt had made the comments at a fringe meeting at the Conservative Party conference last week.
He said: "My wife is Chinese and if we want this to be one of the most successful countries in the world in 20, 30, 40 years time there is a pretty difficult question that we have to answer which is, essentially, are we going to be a country which is prepared to work hard in a way that Asian economies are prepared to work hard, in a way that Americans are prepared to work hard?
"And that is about creating a culture where work is at the heart of our success."
In a statement, issued before Ms Goodman deleted the tweet, a Labour spokesman said: "This does not represent the views of the Labour Party. Helen will be reminded of her responsibilities as an elected Labour politician."
Labour's leader in the House of Lords Lady Smith said Goodman's tweet was "absolutely bizarre".
She told BBC Radio 4's Westminster Hour: "Presumably Mrs Hunt lives in the UK because she's married to Mr Hunt and she's in love with him and wants to be with him so end of story.
"There's a lesson for all here, our partners and families are not in the public domain to be criticised or commented on."
Mr Hunt married his wife, Lucia, in July 2009 and the couple have three children.

Armed police were seen outside a house in the street on Friday morning.
Police said a 30-year-old man had been arrested on suspicion of possession of a class B controlled drug and possessing a class B controlled drug with intent to supply.
The man remains in custody.
A Labour MP has apologised after making comments about Health Secretary Jeremy Hunt's Chinese wife.
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A quantity of suspected cannabis and imitation firearms have been seized by police during a search of a house in Frank Street in east Belfast.