Federer, 37 and bidding for his 101st career title, received a walkover into the final, where he will play Dominic Thiem, a 7-6(3) 6-7(3) 6-4 victor over Milos Raonic in Saturday's only semi-final.
It would have been the first meeting between the pair since 2017.
"I warmed up today and I felt that my knee was not good to compete at the level I needed to compete in semi-final," Spain's Nadal said in a statement.
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"It's tough for me to accept all these things that I'm going through in my career."
The knee had begun to bother him in the second set of his 7-6(2) 7-6(2) victory over Karen Khachanov in the quarter-finals on Friday.
Nadal had enjoyed a dominant week at Indian Wells, reaching the semi-finals without dropping a set.
"For me it is not about today only," the world number two said.
It's about what it means for me to have to pull out in a tournament that I love so much like this one, and in the semi-finals after playing well during the whole tournament. You can imagine that I can't be happy.
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