UEFA said on Tuesday the charges against the two players also include "bringing the sport of football, and UEFA in particular, into disrepute."
Morata and Rodri led thousands of fans singing "Gibraltar is Spanish" at a celebration in Madrid last week after the team's 2-1 win over England in the Euro 2024 final.
Gibraltar, on the southern tip of Spain, has been a British overseas territory for more than 300 years.
The Gibraltar soccer federation filed a formal complaint to UEFA, and has said it welcomed the disciplinary proceedings
"This is an important first step in order to establish the unlawfulness of the chant on the basis of the grounds put forward by the Gibraltar FA in its complaint," the federation said in a statement on Tuesday.
UEFA said its disciplinary body will rule on the case at a later date, with the players facing a possible suspension from Nations League games in September.
Morata completed a move from Atletico Madrid to AC Milan last week. Rodri, who was named player of the tournament at Euro 2024, plays for English Premier League champions Manchester City.
UEFA announced last Friday that an ethics and disciplinary inspector had been appointed to evaluate what had happened at Spain's celebration event in Madrid.
