In the commercial, titled "Inseparable", the man presents a wedding ring to the woman, before saying that they can escape to the north to "a place we can be together across the border".
The short film appears to be set in a southern region of America, during a period of slavery in the country.
The advert's storyline sparked a huge backlash online, with several critics stating that it romanticises the reality of slavery.
One Twitter user pointed out that while some black people may be able to trace their lineage back to white ancestors, in many cases, this is due to the "rampant sexual assault of black women during slavery and Jim Crow".
"I cannot believe that they are airing this commercial. Most 'white' DNA African Americans have was from rape, sexual coercion in the pre civil war years ... most decidedly non consensual," another person tweeted.
"What a horrible commercial. Somebody did not think this one through."
Someone else remarked that for many black Americans, discovering information about their ancestry can be "as painful and traumatic as it is illuminating".
Writer Clint Smith found it odd that the north was depicted as a region where the couple could escape prejudice.
"It is so wild both that this depicting of such a 'relationship' was ever approved for public consumption *and* that they treat the north as some sort of promised land where they will be able to live happily ever after," the scholar tweeted.
"There were clearly no history books at this marketing meeting."
Following the widespread condemnation of the advert, Ancestry.com has taken it down from YouTube and is in the process of removing it from television.
"Ancestry is committed to telling important stories from history," the company told The Independent.
"This ad was intended to represent one of those stories.
"We very much appreciate the feedback we have received and apologise for any offence that the ad may have caused."
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