The Country Liberal Party senator appears in the ad alongside her husband Colin Lillie, who was born in Scotland and recently became an Australian citizen.
The ad was released on Wednesday by the campaign group Fair Australia, which is funded by the conservative lobbying group Advance.
Senator Price was promoted to the shadow cabinet after Liberal MP Julian Leeser resigned from the front bench in order to support the "yes" campaign.
In the nine-minute ad, filmed in her hometown of Alice Springs, Senator Price shares her experience growing up in a blended family with an Indigenous mother and a white father.
"What's important to me is that we don't divide ourselves along the lines of race in this country," she says.
"I don't want to see my family divided along the lines of race because we are a family of human beings and that's the bottom line."
Liberal MP Karen Andrews, who announced her resignation from the coalition frontbench earlier this week, said the party was becoming distracted by the voice debate and needed to focus on cost of living pressures.
Her colleague, opposition treasury spokesman Angus Taylor, agreed with her and said the number one concern for Australians was the cost of living.
"It's our highest priority right now, as an opposition, as a Liberal National coalition ... and it must stay that way," he told ABC radio on Thursday.
"Karen is quite right in saying that."
On Wednesday, Torres Strait Islanders and far north Queenslanders addressed a parliamentary inquiry examining the wording of the proposed constitutional change.
Torres Strait Island Regional Council Mayor Phillemon Mosby said the people of the Torres Strait see the voice as unfinished business.
"We stand with our Aboriginal brothers and sisters of this country, as Torres Strait Islanders, we support the voice to parliament," he said.
"We feel that this is unfinished business and continues the job that was done by our predecessor, the late honourable Eddie Mabo, who overturned the doctrine of terra nullius."
In the ad, Senator Price's husband said he wouldn't stand for a racial line being put through his family.
"Later this year politicians will be asking us to vote on a major change to our constitution. They want to establish a so-called voice to parliament. This is a really big deal," Senator Price added.
"The constitution is the rule book for governing the country and they want the rules to change.
"I'll be voting 'no' because this will not unite us, this will divide us."
The proposed voice would recognise Indigenous Australians in the constitution and establish a body that would advise government on matters that affect Aboriginal and Torres Strait Islander people.
Australians will vote in the referendum on the voice between October and December.
