It happened just after 3 p.m.
Officers went to the area after getting a call about shots fired at 2305 Flowers Road.
They found an armed man and ordered him to drop his gun. Officials said the man pointed the weapon at three officers and they opened fire.
The wounded man, who was identified as 61-year-old Garland Wayne Bass, was taken to UNC Hospitals in Chapel Hill. He was listed in critical condition Tuesday. The deputies were not hurt.
The SBI is investigating the shooting.
Bass is charged with three counts of assault on a law enforcement officer with a firearm.