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McConnell, who faces re-election next year, is married to former labor secretary Elaine Chao. She was born in Taiwan to parents who fled mainland China and immigrated to the United States as a child.
Progress Kentucky, a pressure group opposed to McConnell, posted a message on Twitter that noted that the Senate Republican leader was married to Chao and quipped: "May explain why your job moved to China!"
The group also linked to a press release in which China's Premier Wen Jiabao thanked Chao's father, businessman James Chao, for business deals that helped benefit the Asian economy's shipbuilding industry.
The comments were roundly condemned by Republicans and Democrats, and the group issued an apology late Tuesday, telling a local radio station its messages "included an inappropriate comment on the ethnicity" of Elaine Chao.
Jesse Benton, a spokesman for McConnell's re-election campaign, had earlier called Elaine Chao and her family "shining examples of the American Dream" who came to the United States with little and built successful businesses.
"It is unconscionable that anyone would use blatant race-baiting for political gain," Benton said in a statement.
"Progress Kentucky should be ashamed of themselves. We hope all Americans can agree that these disgusting tactics have no place in American politics as we try to bring people together to solve our difficult problems," he said.
A spokesman for Progress Kentucky had earlier told WFPL, the Louisville radio station that first drew attention to the Twitter posts, that tweets should not be seen in the same way as official statements by the group.
But the group's executive director Shawn Reilly later issued a statement saying: "We apologize to the secretary for that unnecessary comment and have deleted the tweets in question.
"In addition, we have put a review process in place to ensure tweets and other social media communications from Progress Kentucky are reviewed and approved prior to posting."
Chao, who served under former president George W. Bush, worked in the last election as a representative to Asian Americans for Republican Mitt Romney. Polls showed Asian Americans voted overwhelmingly for President Barack Obama.
China is a frequent bugbear in US political ads, which highlight Americans' economic anxieties. Pete Hoekstra, a Republican who unsuccessfully sought a Senate seat in Michigan last year, came under fire for a commercial that featured an Asian girl praising his opponent in broken English.
McConnell is known for his interest in Asia, particularly Myanmar.