Alba underwent tests on Sunday morning that revealed "torn fibres in his right hamstring" according to a statement from the La Liga champions.
The 24-year-old is therefore not expected to be avaialble until after the international break next month, effectively ruling him out of Barcelona's next six games - including the Champions League matches against Ajax and Celtic.
Barcelona were indebted to Alexis Sanchez's last-gasp winner after they had thrown away a 2-0 lead.
Gerardo Martino's side were cruising when Lionel Messi's 75th-minute strike doubled their lead after Dani Alves scored against his former club.
But Ivan Rakitic pulled one back before Coke volleyed in with a minute left to apparently steal a point.
That was until a mazy Messi run forced open the Sevilla defence and when the ball fell kindly to Sanchez he stuck away the chance in the fourth and final minute of added time.
"I was lucky because the ball came to me and I was able to score the match winning goal," Sanchez told Barca TV.
Defender Javier Mascherano admitted, however, that his side had made a lucky escape.
"We were lucky to win but it won't always be this way," he said.
"Everything will get more difficult in the future. We have to improve a lot. It was because of our errors they tied the match.
"What we can't allow is have a two-goal lead and have what happened happen."
Alves revealed his reasons for not celebrating his opener, and admitted Barcelona had almost been stung after wasting a host of chances.
"I don't celebrate goals against Sevilla," he said. "I have special affection for them, they opened the door to Europe for me.
"It was a very intense match, there was a lot of quality on the pitch. They really hurt us with their counter-attacks, but the result had to be ours because we had more chances."