According to the Fort Bend County Sheriff's Office, the shooting happened in the 3300 block of Breeze Bluff Way.
One victim died at the scene. The second person taken to an area hospital in critical condition, but later died.
Fort Bend County Sheriff Troy Nehls said the 911 call came in just before 11 a.m. Officials found the man and woman, both adults, inside the home with apparent gunshot wounds.
The couple's baby boy was in the home at the time. He was not injured. He is being cared for by family members. No one else was in the home at the time of the shooting.
They were initially discovered by the woman's mother, who is described as being distraught.
Nehls said it appeared there had been some type of altercation before the shooting.
The victims' identities have not been released, but they are said to be in their late 20s to early 30s.