"In reference to the agreement made between LaLiga and the company Relevent, which includes that an official league match will be played in the United States, the AFE strongly objects".
The group operates the International Champions Cup, the world's largest summer club tournament.
Interestingly, given the reputation of the two clubs will have been vital to the deal being struck, the Clasico fixture between Barcelona and Real Madrid will not be staged outside of Spain, Tebas confirmed.
La Liga did not give any details on when the first game across the Atlantic was set to take place and did not immediately respond to a request for information from Reuters.
"The agreement marks an inflection point for soccer - the world's most popular sport in numbers of participants and spectators - in the U.S and Canada".
"Joining with Relevent to create LaLiga North America is a major milestone in our global expansion strategy", Oscar Mayo, the league's worldwide development director, said in a statement.
The scheme also seeks to challenge the popularity stronghold of leagues, such as English soccer's Premier League, which is well-watched in the US.
LaLiga North America will be led by chief executive Boris Gartner, a media executive with experience in the US Hispanic and Latin American markets and a former head of strategy and operations at Mexican pay-television operator Televisa.
The Premier League previously considered playing a "39th game" overseas but have been warned fans will fight back just as hard as last time if talks are held again.
Relevant owner and chairman Stephen Ross said: "This extraordinary joint venture is the next giant leap in growing soccer's popularity in North America". The league said it is still making arrangements for the game and there is no timetable for when it will happen, but it could be this season.