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
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.