Fabregas picked up the injury when he came on for the last 10 minutes of Barca's 3-0 Copa del Rey final win over Athletic Bilbao last week before he was named in Spain's final 23-man squad to defend their title in Poland and Ukraine next month.
"Medical tests have been successful, very happy with the evolution," Fabregas wrote on his Twitter feed.
The former Arsenal captain would train away from the rest of the team as he bids to regain fitness in time for Spain's opening Group C match against Italy on June 10, the RFEF said in a statement on their website.
Fabregas began his first season back at Barcelona with a bang but his form deteriorated in the final months of the campaign and coach Pep Guardiola left him out of some key matches in La Liga and the Champions League.
Spain coach Vicente del Bosque has a slew of talented midfielders to choose from and may prefer to start with Manchester City playmaker David Silva alongside Xavi and Andres Iniesta.
Fabregas and his Barca team-mates Xavi, Iniesta, Sergio Busquets, Gerard Pique, Pedro and Victor Valdes, as well as Bilbao pair Fernando Llorente and Javi Martinez, joined up with the squad at Spain's training base outside Madrid on Friday.
Iniesta told reporters he believed Spain's task of retaining their continental title would be harder than winning the World Cup in South Africa two years ago but said the team were ready for the challenge.
"I like to live in the present and to focus on what we have ahead of us," Iniesta said.
"We have a very attractive goal which will be a much greater challenge than the previous one."