Raducanu struggled with the issue in the previous round against Yue Yuan and continued to look uncomfortable in the opening exchanges against the Russian top seed.
The 21-year-old was broken in the second game but, despite breaking straight back, struggled to serve and was unable to chase returns around the court.
She needed a medical time out after the fifth game and decided she could not continue after losing the opening set 6-1.
“I feel sorry for Emma,” said Kasatkina after the match. “It’s a pity to get injured, especially in the deeper stages of the tournament. I wish her a speedy recovery.”
In the semi-finals, Kasatkina beat compatriot Diana Shnaider 6-3 6-4 to set up a final meeting with Beatriz Haddad Maia, who progressed following a 6-4 6-4 victory against Vernika Kudermetova.
Raducanu had been hoping to beat Kasatkina to reach her first semi-final above WTA 250 level since her 2021 US Open victory.
The world number 70 has sustained a number of injuries since her Flushing Meadows triumph.
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