According to police, officers were working in the Hill neighborhood at 5:44 p.m. when they observed a wanted suspect in the area of Greenwich Avenue and First Street.
Police say the suspect attempted to flee on foot and during the encounter, a New Haven officer shot the armed suspect.
The suspect was identified by Connecticut State Police as 21-year-old Marcus Rivera of New Haven.
Medical attention arrived and the suspect was transported to a hospital. The suspect was listed in critical but stable condition.
Officials say a firearm was seized at the scene.
Several streets are closed as officers are holding the scene for investigation into the early hours of Wednesday morning.