Veselý was drafted in the first round by the Washington Wizards with the sixth overall pick in the 2011 NBA Draft. Veselý posted his first double digit scoring night in a 98-77 win over the Detroit Pistons. He finished the night with 10 points, 8 rebounds, and 3 blocks. After Flip Saunders was fired, Veselý saw more minutes on the court under new coach Randy Wittman, who also said that he wants him to shoot the ball a bit more. On April 9, 2012, he recorded his first double-double, finishing the game with 11 points and 11 rebounds in a win over the Bobcats. Veselý continued his success over the Bobcats on April 23, 2012 when he posted a career high 16 points on 8-8 shooting, pulled down 6 rebounds, and recorded 4 steals. He averaged 4.7 points and 4.4 rebounds in his first NBA season.