Couch became known as the "affluenza" teen during his trial in juvenile court, when a psychologist said he was so wealthy and spoiled he could not tell the difference between right and wrong.
A Tarrant County law enforcement official confirmed on Monday that Couch had been detained in Puerto Vallarta, Mexico, but declined to give further details.
CNN, citing officials briefed on the matter, said Couch was with his mother and would be turned over to the U.S. Marshals Service.
Mexico's attorney general's office did not respond immediately to calls seeking information.
At age 16, Couch was speeding and had a blood-alcohol level of nearly three times the legal limit when he lost control of his pickup truck and fatally struck a stranded motorist on the side of the road and three Good Samaritans who had stopped to help.
Several passengers riding in Couch's vehicle were hurt, including one friend who was permanently brain damaged.
Sheriff Dee Anderson said last week it was possible Couch and his mother had fled the country and the home they shared had been cleared of its contents.
Their passports had been reported missing by the teen's father, who has been cooperating with investigators.
Police were checking reports that Couch may have left the United States, after a video came out showing him at a party, in a likely violation of his probation.
U.S. Marshals were offering a $5,000 reward in exchange for his whereabouts.