The American lost 6-1 6-1 to the Czech in the second round at the FitzGerald Tennis Center after replacing compatriot and second seed Mardy Fish in the draw as a lucky loser.
South Africa-born Odesnik was banned for two years after pleading guilty in March last year to importing human growth hormone into Australia - although he denies ever taking the substance.
The ban, backdated to the previous December, was suspended after 12 months. He has since been building up his ranking again on the challenger and futures circuits.
Fifth seed Fernando Verdasco of Spain eased past Australian Marinko Matosevic 6-4 6-4.
Fourth seed Jurgen Melzer and 14th seed Xavier Malisse both retired through injury. Melzer was losing 6-7(6) 6-4 3-1 to American Donald Young when a leg injury ended his tournament while Malisse suffered an arm problem at 7-6(4) 2-3 down against Michael Russell.
Russell and Young will meet in the third round.
Play on Thursday will begin four hours earlier than originally planned.