Dortmund defender Hummels, 32, was named at centre-back with Mueller, 31, leading a three-man attack alongside Bayern Munich colleagues Leroy Sane and Serge Gnabry.
It is their first international appearance since the 2014 World Cup winners played in a 2-2 draw in the Nations League against the Netherlands in November 2018.
Germany coach Joachim Loew had made the decision to drop Mueller and Hummels from the national side in March 2019, following the team’s group stage exit at the World Cup in Russia.
Loew, who steps down later this summer after 15 years in charge, has recalled the experienced pair for the European Championship, which runs from June 11-July 11.
Germany play a final pre-tournament friendly against Latvia on Monday before hosting world champions France in Munich on June 15 in their opening match of Euro 2020.