Alba was replaced with 11 minutes remaining in Spain's 1-0 triumph over Ukraine in Euro 2016 qualifying on Friday, and Del Bosque claimed the 26-year-old's early departure let the visitors back into the match.
Del Bosque confirmed the full-back will return to Barcelona on Saturday for tests.
"Our doctors are in touch with Barcelona's medical team, he's leaving the national team for now, and tomorrow he will be in Barcelona for the correspondent medical check-ups," the veteran coach said.
Del Bosque added: "Our full-backs were brilliant until Jordi Alba's injury.
"I'm sure it was because Andriy Yarmolenko had to defend less after Jordi left the pitch.
"Juanfran played great but he had a lot of work with his defender [Yevhen Konoplyanka] so he had less activity in offence."
Spain won thanks to Alvaro Morata's 28th-minute goal but Del Bosque was less than pleased with his side's second-half display.
The 64-year-old argued that his team moved less after the break and seemed to lack fitness, while he indicated Ukraine's desperation for an equaliser inhibited Spain.
Spain's win saw them move three points clear in second in Group C, with Ukraine (nine points) in third, while Slovakia (15) top the standings after a 3-0 victory against Luxembourg on Friday.
"Ukraine pressured in our side of the pitch in the second half, when they were down a goal," Del Bosque said.
"We found it difficult to create play, too many passes to Iker [Casillas], too many passes to [Gerard] Pique, and few passes forward.
"As I said before, we lacked mobility in front of the ball, and that made it hard for us to play well in the second half."
