"They did some tests yesterday and the doctors saw that he (Fabregas) is in reasonably good shape," Del Bosque told a news conference in Seville previewing Spain's final warm-up match against China on Sunday.
"He will rejoin the rest of his team mates in training at some point and, possibly, be ready for the 10th," he added.
Fabregas, who will be rested against China as a precaution, sustained the injury during Barcelona's 3-0 Copa el Rey win over Athletic Bilbao last month before he was named in the world champions' 23-man squad to defend their continental title in Poland and Ukraine.
The former Arsenal captain was one of a number of Barca players who ended an intense season carrying injuries and central defender Carles Puyol has been ruled out of Euro 2012 after needing knee surgery.
Midfield orchestrator Xavi, a key player in Spain's triumphs at Euro 2008 and the 2010 World Cup, has been suffering from a persistent calf problem but told a separate news conference in Seville on Saturday he was back to full fitness.
"I am in very good shape and very pleased, excited and physically fine," the 32-year-old said.
"Yesterday I trained (with the national team) for the first time, I played the Copa del Rey final, and I was already feeling good at Real Betis on the final day of the La Liga season (on May 12)," he added.
"I am ready to compete and to make history again with the national team."
Spain are bidding to become the first nation to win back-to-back continental titles with a World Cup in between and Prime Minister Mariano Rajoy told the players on Friday another victory would help lift the struggling Iberian nation out of its economic gloom.
Del Bosque said he and his players were aware of the wave of euphoria among Spanish fans about the team's prospects.
"We are under a lot of pressure because the optimism around us is excessive," he said.
"There are 16 very good teams and it will not be a walk in the park, but we are used to pressure because we are defending the title and we are world champions.
"In any case, if we win the European Championship it will not be the solution to Spain's problems."