Abdus-Salaam died from drowning in the Hudson River, the statement said.
Friends and colleagues described the judge as a trailblazer and pioneer.
Her life had also been marked by personal tragedy. Her brother committed suicide three years ago, two law enforcement sources told CNN.
Abdus-Salaam, 65, had also been stressed recently at work, the sources said. Her body was found April 13. Detectives did not find a suicide note.
The judge was last heard from about 9 a.m. the previous day, according to the sources. Abdus-Salaam's husband told police his wife's secretary received a call from the judge saying she wouldn't be at work that day.
Police responded to a 911 call about a person floating in the Hudson around 1:45 p.m. They found an unconscious and unresponsive woman, who was later pronounced dead and identified as Abdus-Salaam. She was fully clothed in running attire, a black hooded sweatshirt, sweatpants and sneakers.
'A true pioneer'
Manhattan District Attorney Cyrus Vance Jr. called her "a true pioneer and leader in the justice system," who "lived up to her reputation of being smart, principled, and rigorously fair."
"Justice Abdus-Salaam leaves a void not only on the state's highest bench, but in the criminal justice system as a whole," he said in a statement.
Born in Washington to working-class parents, Abdus-Salaam grew up with six siblings and attended the district's public schools.
She became interested in pursuing law after civil rights attorney Frankie Muse Freeman visited her high school. Abdus-Salaam attended Barnard College for her bachelor's degree and later received her law degree from Columbia University.
She began her legal career at the East Brooklyn Legal Services and later became an assistant attorney general in the New York State Department of Law.
She began her judicial career in 1991 and was appointed in 2009 by Gov. David Paterson to the Appellate Division, First Department.
"During her time on the bench, Justice Abdus-Salaam earned the respect of all who appeared before her as a thoughtful, thorough, and fair jurist," New York Attorney General Eric Schneiderman said in a statement.
Gillian Lester, dean of Columbia Law School, said Abdus-Salaam spoke recently at the school's "Empowering Women of Color" conference. On Tuesday, the judge was to be the featured speaker at the annual alumni of color gathering, Lester wrote on the law school website. The event will be postponed "in light of this terrible loss."
Abdus-Salaam was awarded the law school's Lawrence A. Wien Prize for Social Responsibility in 2013.
"Sheila Abdus-Salaam set an example for generations to come, as much for her brilliance, moral conviction, and remarkable professional achievements as for her kindness, modesty, and understated yet unfailing generosity," Lester wrote.