Authorities said they were called around 6 a.m. to the woods in the vicinity of Atlas Post Acute on Cooper Street for what was reported as a traumatic injury.
The 65-year-old man was taken to a local hospital for treatment, and officials said his injuries were not life-threatening.
Police said the attack may have been targeted and emphasized that they do not believe there is any danger to the public. No arrests have been made.
Neighbors who live near the wooded area, which backs up to several residences, said they were surprised by the unusual incident and later saw officers canvassing the neighborhood and asking for doorbell camera footage.
"Kind of a weird situation, you know, not something you hear about every day, especially in a quiet community like this," said Matt Duffield, a Woodbury resident.
Others expressed fear over what could have happened.
"What would've happened if he didn't survive. He would've been left in our woods, and that makes me very scared," said Shana Jordan, who lives nearby.
Police have not released the man's identity. However, several neighbors said they believe the victim is a homeless man who frequents the area.
"I would like to see him get some help," Jordan said.
The use of a bow and arrow also concerned residents.
"It makes me go, 'Someone did something that they kind of knew what they were doing,'" Jordan said.
An administrator at Atlas Post Acute said the incident did not involve anyone at the facility.
The police chief noted that when officers encounter individuals experiencing homelessness, they offer them available resources.
Anyone with information is asked to contact Detective Corporal Nicholas Cacciola at 856-845-0065 ext. 142.