The men, aged 18 and 26, have been arrested in connection with an incident which took place in Ellers Grove, Harehills, on Wednesday night.
Police found a bullet lodged in the door to the home after forensics officers examined the scene.
Bullet lodged in door after gunshot fired at home in LeedsThe 26-year-old man was arrested from an address in Harehills by armed officers shortly after 7pm last night.
A police spokesman said: "Prior to attending the address, officers assembled near to St James's Hospital, and we are aware this activity has been the subject of speculation on social media about a vehicle being stopped there at gunpoint.
"This was not the case and we hope this update will clarify the situation."