Warner, 54, was vacationing in Costa Rica with his family, media reported. The Central American nation's judicial investigation department (OIJ) confirmed that a United States citizen with the last name Warner had drowned after being pulled out to sea by a rip current.
He was declared lifeless at the scene by Red Cross lifeguards, the department said.
Representatives for Warner did not immediately respond to requests for comment.
The NAACP posted a photo of the late actor on Instagram along with a caption.
"#RestinPower, to NAACP Image Award winning actor, Malcolm-Jamal Warner. Your talent and spirit touched many lives, and your legacy will continue to inspire," the caption said.
Warner won the outstanding actor in a comedy series award from the NAACP for the series Reed Between the Lines in 2012.
Fox Entertainment also issued a statement on Monday about Warner's passing.
"Everyone at FOX is heartbroken by the tragic loss of our friend and colleague, the extraordinary Malcolm-Jamal Warner. While his iconic roles - from comedic to dramatic - are unforgettable and timeless," the statement said.
Warner played Dr AJ Austin on the Fox medical drama series The Resident.
The Cosby Show, which aired from 1984 to 1992, was one of the earliest portrayals of a successful, stable and wholesome black American family on television, which challenged negative stereotypes. Cosby portrayed a doctor, and Warner played his only son.
Warner, who was born on August 18 in 1970, grew up in Jersey City, New Jersey, with his mother, Pamela, who eventually became his acting manager. He was named after civil rights leader Malcolm X and jazz musician Ahmad Jamal.
At an early age, Warner found he was interested in acting, which launched his career as a child performer and set him on the path to attend The Professional Children's School in New York.
While he had some small TV roles early in his career, playing Theo Huxtable on The Cosby Show served as Warner's breakout role.
The actor received an Emmy nomination in 1986 for outstanding supporting actor in a comedy series for his role on the NBC series.
The 54-year-old actor also had roles in The Cosby Show spin-off series A Different World, Jeremiah, Sons of Anarchy, Suits and hosted Saturday Night Live in 1986.
He is survived by a wife and daughter but he never publicly disclosed their names.
