Donald Trump, Jeb Bush and Scott Walker will take the stage in Cleveland on Thursday night with seven rivals.
Fox News selected the 10 most popular Republicans based on five national polls, excluding Mr Perry and South Carolina Senator Lindsey Graham.
Those two and five other candidates will take part in an earlier debate.
Former Pennsylvania Senator Rick Santorum reacted angrily to his omission.
"The idea that they have left out the runner-up for the 2012 nomination [Santorum], the former four-term governor of Texas [Perry], the governor of Louisiana [Bobby Jindal], the first female Fortune 50 CEO [Carly Fiorina], and the 3-term Senator from South Carolina [Graham] due to polling seven months before a single vote is cast is preposterous," his spokesman said.
In contrast, Mr Perry tweeted that he was looking forward to being on Fox at 5pm for "a serious exchange of ideas and positive solutions to get America back on track".
The main debate takes place four hours later at 9pm local time (01:00 GMT).
All eyes will be on hotel tycoon Mr Trump, who leads the polls and has made headlines with outspoken remarks about many of his rivals.
A fun guide to the 10 Republican debaters
One of the Republican frontrunners, Jeb Bush, became embroiled in a row with leading Democratic candidate Hillary Clinton over women's health funding on Tuesday.
The former Florida governor was attacked by Mrs Clinton after he told a conservative Christian audience he wasn't sure "we need half a billion dollars for women's health issues".
But he later said he "misspoke" after criticism of his remarks.
Meet all of the 2016 hopefuls

The City Council wants to add an extra 700 spaces to the east of the Seacourt site, which currently has 794 spaces in an attempt to ease congestion.
Proposals include a new waiting area building and increased cycle parking.
The council said it considered relocating to a lower flood-risk zone but had not been able to find a suitable alternative.
A spokesman said: "The proposals respond to the rapid growth that is anticipated in the city centre, particularly the west end regeneration area."
The site, which serves users entering from the west of the city, has been operating for more than 30 years.
Subject to planning consent, work could start in Spring 2016 with the complex anticipated to be open in the Summer of 2017.
A public exhibition is being held at the Assembly Room at Oxford's Town Hall.
There will be a further session on 19 September at the West Oxford Community Centre.
Rick Perry, the former governor of Texas, is not among the 10 Republicans running for president who will take part in the first primetime TV debate.
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Plans to expand one of Oxford's Park and Rides into the Green Belt have been unveiled.