Police say the carnage began around 8 a.m. on West 65th Street in Riverside Park, when the suspect, identified as 43-year-old Julius Graham, stabbed a 36-year-old female jogger in the back on the running path.
It is believed Graham, who is homeless and originally from Texas, was brandishing scissors.
Police say Graham then moved south and stabbed a 36-year-old man, who was walking his dog, in the stomach. He continued south down the bike path along the Hudson River, slashing a 32-year-old female jogger in the neck before coming upon 35-year old James Fayette and his two year old son Luke in a stroller.
Fayette was slashed in the chest while trying to protect his son, who suffered a slash wound to his arm. The child's stroller sat in the middle of the crime scene, surrounded by police tape.
"The baby was screaming, the father was shielding him, the father was covered in blood, and he was doing the best to protect his kid," said eyewitness Billy Bednarz.
James Fayette eventually subdued the suspect with the help of a bystander.
"A good Samaritan saw what was going on, tackled the guy, got him to the ground and held him until the cops arrived," said Bednarz.
Police arrived and found Graham being restrained on the ground.
"He was going crazy, resisting arrest, there were three cops on him. It was insane," said eyewitness Jennifer Wenzell.
The victims, four of whom were taken to Roosevelt Hospital, were all expected to survive, though one of the women was listed in critical condition.
The incident occurred along the Hudson River Greenway, a 32-mile long stretch used for biking and walking, beneath the Henry Hudson Parkway.
Graham, who was staying in a shelter in the Bronx last week, was taken to Bellevue Medical Center for psychiatric treatment.
Graham is charged with five counts of assault, criminal possession of a weapon, and resisting arrest.
Fayette is a former principal dancer with the New York City Ballet. He is married to Jennifer Ringer, a current principal dancer with the ballet.
Fayette will remain in intensive care at least overnight, while his son has been released from the hospital.
Geoffrey Croft, a spokesman for New York City Park Advocates, called the attack the latest episode in a "troubling trend" of violence in city parks.
He noted that a mother pushing a stroller along the Henry Hudson Parkway in Fort Tryon Park in Upper Manhattan was attacked by a homeless man last week. At least two bicyclists were attacked a week apart in August along the Hudson River around 163rd Street, and two other people were slashed south of 60th Street a month earlier, Croft said.
Croft said the advocacy group has been calling for more park enforcement for years. Citywide, he said there are 80 security officers patrolling the city's parks, with another 80 recently hired. In the 1990s, there were 450 parks security officers, he said.
When asked about the spate of recent attacks, the police commissioner said city parks are "very, very safe." He said that although authorities are concerned about the recent crime, "the amount of incidents of crime in parks is minuscule."
The Associated Press contributed to this report.