Abdus-Salaam was discovered fully clothed on the Manhattan side of the river on Wednesday – a mile from her central Harlem home – a day after she was reported missing by her husband.
Police said her body showed no obvious signs of trauma or injuries indicating foul play and that a post-mortem examination would determine the cause of death, local media reported.
New York’s governor, Andrew Cuomo, while eulogising the deceased, said he was proud to have appointed her to the state’s highest court, adding he was “deeply saddened by her passing”.
He described her as a “trailblazing jurist whose life in public service was in pursuit of a more fair and more just New York for all”.
“She was a pioneer,” he said. “Through her writings, her wisdom, and her unshakeable moral compass, she was a force for good whose legacy will be felt for years to come.
“On behalf of all New Yorkers, I extend my sympathies to her family, loved ones and colleagues during this trying and difficult time.”
New York Mayor, Bill de Blasio, wrote on Twitter: “Deeply saddened by the tragic passing of Sheila Abdus-Salaam. She was a humble pioneer. My thoughts are with her family.”
The Princeton Encyclopedia of American Political History said she was the first Muslim woman to serve as a US judge.
Born in Washington DC, Abdus-Salaam graduated from Columbia Law School and began her career in law working at East Brooklyn Legal Services as a staff lawyer.
The 65-year-old rose through the ranks and was elected to the Supreme Court in 1993 to be the first African-American woman to serve on New York’s highest court.
She was also an associate judge of the Court of Appeals.