The Barcelona playmaker sustained the injury in last month's King's Cup final but was able to take part in Spain's final session in Madrid before they fly out to their Euro 2012 training base in Gniewino, Poland later on Tuesday.
He should be available for the holders' opening Group C match against Italy in Gdansk on Sunday, although he is not guaranteed a starting spot in a squad with a host of hugely talented midfielders.
Alvaro Arbeloa, a regular at right-back under coach Vicente del Bosque, has a minor neck injury and had to train apart from the rest of the squad, the Spanish football federation (RFEF) said in a statement on their website.
If Arbeloa fails to recover in time for Sunday Del Bosque will likely deploy Juanfran, a recent addition to the roster who made his debut in a friendly against Serbia last month.
Winger Jesus Navas had to be taken for a precautionary scan on his right hand after receiving a blow but it showed he had not suffered any significant bone damage, the federation added.
Navas has mostly been used off the bench as an impact player and is unlikely to be in the starting line-up against Italy.
Fabregas and some of his team-mates were back using Twitter on Monday after an initial ban on using social networking sites was lifted.
"Good news! Finally we are allowed to use social networks so we will be in contact during the Euro Cup," Fabregas, one of Spain's most committed Tweeters, wrote on his feed.
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