Police were called to a Mission, Texas, home after the family's black Labrador retriever came home Thursday with the hand, the San Antonio Express-News reported.
The body of a man was discovered near a canal after a 2 1/2-hour search, the newspaper said.
Police Sgt. Jody Tittle said the body likely was there for two or three weeks, and documentation with the body indicated he was an immigrant.
The case is being treated as a homicide pending autopsy, and police have asked the Mexican consulate for help in identifying the man.