McLaren said their cars would also carry an 'End Racism' message.
"Our first race in Austria at the start of July is a big moment for our sport after nearly four months of no racing," said Formula One chairman Chase Carey in a statement.
"It is also a time to recognise the issues that are bigger than any one sport or country.
Formula One will stand united to say loud and clear that racism must end. We will show our full support in fighting inequality throughout the weekend and accelerate our own efforts to make Formula One more diverse and inclusive.
Toto Wolff on how Lewis Hamilton encouraged him to recognise problems around race in Formula One
Austria's Red Bull Ring is hosting two races on July 5 and 12 after the long break caused by the COVID-19 pandemic.
Formula One said the task force would listen to a range of people, including drivers, to identify what needed to be done to improve diversity and opportunity.
Six-times world champion Lewis Hamilton, who took part in a Black Lives Matter march in London at the weekend, has stepped up his anti-racism campaigning.
He announced on Sunday a commission to help motorsport engage more young people from black backgrounds and drive diversity.
The Briton has also called out his sport's initial silence over the killing of George Floyd, an unarmed black man who died in Minneapolis after a white U.S. police officer knelt on his neck last month.