The Chile international limped off at the end of Barca's 3-1 home win over Sporting Gijon after having come on as a second-half substitute, and will miss their Champions League last 16 second leg at home to Bayer Leverkusen on Wednesday.
"Alexis is 22, he has to develop and know what it is to play every three days," coach Pep Guardiola told reporters. "But he is a vital player and we will miss him. It is one more hurdle to overcome."
Aside from the injury to Alexis, Guardiola said he was pleased with the way his players recovered from Gerard Pique's sending off early in the second half to win, and picked out midfielder Seydou Keita for special praise.
The Malian, starting for the first time since November, struck a curling shot into the top corner to put Barca 2-1 ahead in the 79th minute. It was his first league goal this season.
"He didn't just score a goal, it was a fantastic goal," Guardiola said.
"There are many players who feel offended when they don't get to play, as if they were the centre of the universe. When you ask me why I like Keita so much it is because every time I bring him on for a few minutes he makes the most of it.
"He knows he is competing with some great players but when he plays like he did today it makes me quite emotional. I hope he can stay with us for a long time."
Champions Barca closed the gap on leaders Real Madrid to seven points, with Jose Mourinho's team not playing at home to Espanyol until Sunday.
"We still have a huge challenge in front of us, which is to stay in the race, to be there, to be strong " said Guardiola.
"I don't have that much belief that we can do it, but Madrid still have to come here and fight for this league title."
