Bronze suffered the injury during Barcelona's 1-0 semi-final first-leg win over Chelsea at Stamford Bridge last week as she went down clutching her knee before receiving medical attention on the pitch.
The English international, who previously won the Champions League three times with Olympique Lyonnais, has been ruled out of the second leg on Thursday and her return to action will depend on her rehabilitation progress, the club said.
"She has a strain, an ailment. It's a tiny intervention, just a couple of weeks," Giraldez told a news conference.
"Lucy has been important for us. We have plenty of players here and I know we have players that can step in."
Bronze posted a photo of her from the hospital bed on Twitter, saying she was in "very good spirits" following the surgery. "Currently working hard towards a speedy recovery to get back on the pitch with my team," she added.
England will be without captain Leah Williamson and Beth Mead at the July 20-Aug. 20 World Cup in Australia and New Zealand after they suffered a ruptured anterior cruciate ligament.
There are also doubts over the availability of forward Fran Kirby and defender Millie Bright.
European champions England are in Group D along with Haiti, Denmark and China.
