Police say the victims' son-in-law, 35-year-old Albert Torres, was taken into custody on Friday evening.
The attack happened inside a home on East 69th Street in the Bergen Beach neighborhood.
Authorities say they received a 911 call just after 7:30 p.m. Thursday.
Both victims suffered multiple stab wounds and were taken to Brookdale University Hospital. Juan Manuel Galicia, 49, died at the hospital, while his wife, also 49, remains in critical condition.
Investigators say that shortly after the stabbing, the suspect called a family member and said, "I've taken care of your parents." That person then alerted another relative, who called 911.
Neighbors who spoke with Eyewitness News said they don't know too much about the couple, but were stunned to hear what happened.
"I'm shocked because this is usually a quiet, safe neighborhood," one woman said.
Police described the suspect as a man , 5'6" tall, last seen wearing blue pants and a white hooded sweatshirt. He allegedly fled the scene in a blue Toyota SUV and remains at large.
It's not clear yet what the motive is.
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