The matter will come before court on Friday.
The institution has also been slammed by organisations and sex worker advocacy groups for exhibiting the work of convicted artist Zwelethu Mthethwa, who was found guilty of murdering sex worker Nokuphila Kumalo on 16 May.
Mthethwa is being sentenced in the Cape High Court today.
The party wants the gallery to be charged with contravening hate speech laws and demanded they pay a R150 000 fine.
They also want the exhibit removed and demand a public apology “for the harm caused”.
In January, party members protested in the gallery by placing a sticker over the exhibit, saying “Love Thy Neighbour”.
The exhibition was created by artist Dean Hutton, who is a white “gender-queer”.
The exhibit was inspired by the #FeesMustFall movement, where the artist at the time photographed a student wearing a T-shirt with text “F*** White People”.
Cape Party leader Jack Miller slammed the museum, saying: “We expect the government-funded gallery to issue a public apology and pay a fine of R150 000, as this was the same ruling given to Penny Sparrow for her racist public comments”.
But Rooksana Omar, chief executive of Iziko Museums, said Miller was looking for publicity.