Spaniard Robredo, a former world number five, has been troubled by the injury for a month and he aggravated it in the second set of his 6-1 6-3 fourth-round victory over American Sam Querrey on Wednesday.
"I knew I was not going to be able to play, so that's why I pulled out," the 25th seed Spaniard said. "We did an MRI last night, and we saw the results.
"The doctor here says not to play. We have been delaying it as much as possible because we were contacting our doctors in Spain to see what they feel about. Now the decision is done."
Robredo, who has a win-loss record of 16-4 this season, said he had also withdrawn from the ATP tournament in Miami starting next week.
"I have a strained muscle in two places, so no chance to play," the Spaniard added. "Well, a chance to play, yes, but then for sure I wouldn't be running as normal and I will have the chance to break it.
"It's not an easy situation for a player, playing as good as I was playing, and I was hoping to try to reach the semi-finals. But when you are not 100 percent, then you have no chances."
Del Potro, while expressing regret for the Spaniard's plight, looked forward to a possible match with world number one Nadal in the last four at Indian Wells.
"Of course I'm sorry for Robredo and I wish him a fast recovery," said the 22-year-old Argentine, who won his eighth ATP title at last month's Delray Beach International Championships.
"But I am glad to be in the semi-finals. Maybe I could play with Nadal again. We make very good matches before, so I have two days to be better, in good form, and hopefully I can play 100 per cent."
Del Potro has a 3-4 career record against Nadal, having beaten the Spaniard 6-2 6-2 6-2 in the semi-finals of the 2009 US Open where he went on to win his first grand slam title.
"It was two years ago, and I think he's playing better today," said del Potro, who played just three tournaments last year because of an injury to his right wrist.
"I'm not the same player as two years ago, but I have improved my game since two months ago."