The Federal Aviation Administration is investigating the crash of a small plane into a house in the Houston area on Monday morning.

The agency said the plane, a Piper J3C-65, struck the house in Fulshear, Texas, around 6:45 a.m. local time.

It was not immediately clear if the house was occupied at the time. The pilot, who was identified as Alan Gillis, was the only person aboard the plane when it crashed, officials said. Mr. Gillis, of Richmond, Texas, was taken to Memorial Hermann Katy Hospital in Katy, Texas, where he was listed in serious condition on Tuesday, according to a hospital spokesman.

The cause of the crash was under investigation. It occurred in a neighborhood near the Covey Trails Airstrip in Fort Bend County, about 33 miles west of Houston, the Fulshear Simonton Fire Department said.

Several agencies, including the Texas Department of Public Safety and the Fort Bend County Sheriff’s Office, responded to the scene. The Fulshear Simonton Fire Department shared a photo on Facebook showing the small, yellow propeller plane sitting at an angle by the pool in the backyard of the single-family home.

The left wing was on the ground and the right wing was leaning against the roof. The fire department and Sgt. Stephen Woodard of the Texas Department of Public Safety referred inquiries about the crash to the F.A.A.

Public records show that the residence is owned by Paul E. Tsika Ministries, a Christian organization run by Paul and Billie Kaye Tsika. Reached by phone, Mr. Tsika referred inquiries about the crash to the F.A.A.

Susan C. Beachy contributed research.