Morata had an MRI scan on Sunday after limping off during Chelsea's 1-0 Premier League home defeat by Manchester City on Saturday.
Morata will fill Costa void for Chelsea, says Shevchenko
According to British media reports on Tuesday, the injury could keep him out for at least six weeks.
Spain manager Julian Lopetegui on Monday called up 36-year-old Athletic Bilbao striker Aritz Aduriz to replace Morata, with the Blues forward missing Spain's final World Cup 2018 qualifying matches against Albania and Israel.
Spain are also missing injured duo Andres Iniesta of Barcelona and Dani Carvajal of Real Madrid, replaced by Las Palmas' Jonathan Viera and Real Sociedad's Avaro Odriozola, as the Group G leaders bid to earn a place at the finals in Russia.
Morata reiterates desire to repay Conte faith
The Spaniards are three points clear of second-placed Italy with just the two rounds of matches remaining.
Chelsea signed Morata from Real Madrid in the close season and the striker has flourished at Stamford Bridge, with seven goals in nine appearances for Antonio Conte's champions.
If Morata's worst fears are confirmed, he will miss both of Chelsea's Champions League group stage matches against AS Roma and several Premier League games, including the home clash with Manchester United on November 5.
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