Standing 6 ft 6 in, Meschery also was a highly talented basketball player. After graduating from St. Mary's, he was drafted by the Philadelphia Warriors as the 7th pick overall in the 1961 NBA draft. Meschery played alongside legend Wilt Chamberlain, to whom he later dedicated a poem. Meschery was the starting forward on the 1961-62 Philadelphia Warriors team in which Chamberlain scored 100 points. Meschery led the NBA in personal fouls in 1962 and he became the first foreign born player to play in an NBA All-Star Game when he played in the 1963 NBA All-Star Game. Chamberlain left the Warriors in 1965, returning to his home town Philadelphia, to play with the 76ers. The Warriors however, strengthened by the arrival of Rick Barry, made it to the 1967 NBA Finals, in which they lost to Chamberlain's 76ers. After his NBA Finals appearance, Meschery was selected by the NBA's Seattle SuperSonics during the 1967 NBA Expansion Draft.