Visitors to the Washington DC gallery throw crumbs for the model to clean.
The gallery says Ivanka Vacuuming, by Jennifer Rubell, explores Ms Trump's "comically wide range of feminine identities - daughter, wife, mother, sister, model, working woman, blonde".
In response, Ms Trump tweeted that "women can choose to knock each other down or build each other up".
The performance is being staged by arts group CulturalDC for two hours every night until 17 February, and is also being live-streamed online.
CulturalDC's executive director Kristi Maiselman said Ms Rubell's work was "insightful", "timely" and "boundary-pushing" in its reflection of contemporary womanhood.
The gallery added that it was not just about Ms Trump, and did not represent "one feeling, one relationship or one point of view towards this powerful and sexualised female form".
But Ms Trump - the president's daughter and a White House adviser - disagrees.
Tweeting almost a week after the piece launched, she accused the artist of trying to "knock down" a fellow woman.
Her brothers reacted in a similar way.
Donald Trump Jr called the piece a "sexist attack", while Eric Trump told Fox News that his sister was "a powerful woman who has done more for women than probably anybody in Washington DC".
Replying directly to Ms Trump online, Ms Rubell said she would like for her to "form [her] own direct response". The artwork is not intended to mock, she added, but is instead "exploring complicated subjects we all care about".
She also offered to arrange a private visit for Ms Trump "with none of the media circus that has formed around it".
In an interview on CulturalDC's website, published before its launch, Ms Rubell said the piece was also partly about power and control.
"Here's what's complicated: we enjoy throwing the crumbs for Ivanka to vacuum. That is the icky truth at the centre of the work. It's funny, it's pleasurable, it makes us feel powerful, and we want to do it more," she says.
"We like having the power to elicit a specific and certain response. Also we know she'll keep vacuuming whether we do it or not, so it's not really our fault, right?"