The victim, believed to be a man in his 60s, has yet to be formally identified following the mid-morning incident in Crawley, according to police.
Police said he was treated by paramedics for serious injuries, but was later pronounced dead at the scene, on a path close to a playground in Cherry Lane.
Witnesses are being sought to the incident which was reported to police at about 10.30am.
Police said a 22-year-old man from Crawley was arrested shortly afterwards at the nearby bowls pavilion in connection with the incident on suspicion of attempted murder.
Last night, Sussex Police confirmed the man had been rearrested following the victim’s death on suspicion of murder and remained in police custody.
Detective Chief Inspector Mike Ashcroft from the Surrey & Sussex Major Crime Team, who is leading the investigation, said: “At this time we are attempting to identify the victim of this attack and considerable forensic evidence is being secured at the scene.
“There is a man in custody and I am appealing to anyone who may have information about this incident to come forward and speak to the police.”
Anyone with any information about the stabbing is asked to report it online or call 101 quoting Operation Hale.
Alternatively, visit the Crimestoppers website or contact the independent charity anonymously on 0800 555 111.
Crawley Borough Council has announced that the playground will be closed for the rest of this week.
“The Play Service will re-open next week on Tuesday 5 December at Creasys Drive Adventure Playground,” the council said in a statement.