There's no visible damage on the small plane, which set down in the grass next to the pavement along State of Texas Vista Road, close to entrance of the park.
The pilot was flying from the airport in Beach City, next to Baytown. The plane is used to patrol pipelines, as a type of private security force.
The aircraft lost oil pressure, and the pilot opted to land on the park road, as he was too far from any airport.
"The road was clear; didn't see anybody on the road. The road was pretty much just a runway so it made a pretty uneventful landing on the road and that's basically how it went," said pilot Travis Ponder.
No one was injured.
The monument is scheduled to be open for visitors today.
The plane has been loaded up and taken to a storage facility nearby.