The 125-pound fight will consist of three rounds and take place on UFC Fight Night at a location to be announced.
Barber (8-2) is seeking her first win since October 2019, when she knocked out Gillian Robertson in the first round. The 22-year-old tore her ACL in her next bout, a decision loss to Roxanne Modafferi at UFC 246 in January 2020. Barber returned from the knee injury in February and suffered a decision loss to Alexa Grasso.
Fighting out of Chicago, Barber started her UFC career 3-0 before dropping her past two bouts.
Maverick (9-2) has looked very impressive since joining the UFC last year. The 23-year-old is coming off a convincing win over Robertson at UFC 260 last month in Las Vegas that improved her UFC record to 2-0. Maverick defeated Liana Jojua in her debut via knockout in October.
The UFC has not yet announced a main event for the July 24 card.