Jami Durham, assistant director of historic properties for the foundation, said she noticed the statue missing when she walked up to the front of the mansion Tuesday morning. Usually two of the 116-year-old statues are there.
But Durham said she believed the theft happened sometime last Thursday night.
"One of our workers told me he saw it missing Friday," she said. "He thought we had taken it in for repair work."
Police described the griffin as about 34 inches tall, with raised lettering on the bottom that reads, "J.L. Mott Iron Works NY."
Bishop's Palace, originally known as Gresham's Castle, was built from 1886 to 1892 by Walter Gresham, a wealthy Galveston attorney.
Police ask that anyone with information on the stolen sculpture's whereabouts call detective Jason Chide at 409-765-3773.