The Tik Tok singer claims she is a "slave" to Sony and that Dr Luke committed a hate crime against her.
But Supreme Court Justice Shirley Werner Kornreich said: "Her claims of insults about her value as an artist, her looks and her weight are insufficient to constitute extreme, outrageous conduct intolerable in a civilised society."
The judgement added: "Every rape is not a gender-motivated hate crime."
Kesha says she was drugged and sexually and emotionally abused by the producer during 10 years of working together.
Dr Luke, real name Lukasz Gottwald, denies the allegations and has not been charged with any crime.
He says Kesha is fabricating accusations to escape a five-album contract.
"Kesha and I were friends for many years and she was like my little sister," he wrote on Twitter in February.
Kesha is still free to continue fighting contract issues.
The 29-year-old has had support from other stars including Taylor Swift and Adele with the hashtag #FreeKesha trending on Twitter.
Sony has said it has made it possible for Kesha to record music without Dr Luke but that it cannot terminate a contract between the singer and producer.