Duran, the Big 12 Player of the Year, was taken in the sixth round (188th overall) by the Milwaukee Brewers.
The draft continues Friday. Another five to seven A&M players are expected to be selected.
The Aggies will be in Houston on Friday, preparing for their NCAA Super Regional series against Rice at Reckling Park.
Duran, a junior who has started all 63 games at shortstop for the Aggies, leads the team in hitting at .382, is second in RBIs with 67 and second with 167 total bases. Duran also has 66 runs, seven triples, six homers and 14 stolen bases
Duran's brother, German, is a member of the Texas Rangers organization and is playing at Triple-A Oklahoma City after a brief stint this season with the Rangers.
Seven other Big 12 players were selected on the first day, including Aaron Crow, Missouri's right-handed ace who was taken with the ninth pick by the Washington Nationals.
The Nationals also selected Blinn JC right-handed pitcher Paul Demney in the sixth round. Demney is a freshman from East Bernard.
Other Big 12 players chosen on the first day were Oklahoma State shortstop Jordy Mercer (3rd round, Pittsburgh), Texas Tech right-fielder Roger Kieschnick (3rd round, San Francisco) and relief pitcher Zachery Stewart (3rd, Cincinnati), Texas right-fielder Kyle Russell (3rd, Los Angeles Dodgers), Nebraska right-hander Ben Pribanic (3rd, Seattle) and Missouri left-handed starter Rick Zagone (5th, Baltimore).