"The Texas EquuSearch team found Jose's wrecked vehicle, with him inside. Amazingly, Jose is badly injured, but still alive," officials said in a statement.
Velazquez's fiancee, Chanel Nelson, told KTRK she last saw Velazquez after they left the bar on Main Street in Houston.
Velazquez's cousin said Nelson joined her fiancee at the hospital Sunday.
"He's laughing and making jokes," Tony Velazquez told the Chronicle.