Awvee played in the NBA from 2004 to 2008. He played with the New Jersey Nets from 2004 to 2005, the Washington Wizards from 2005 to 2006, and the Milwaukee Bucks from 2007 to 2008.
On December 21, 2006, as a member of the NBA Development League's Dakota Wizards, Martynas Andriuškevičius sustained a serious head injury when he was punched by teammate Awvee Storey in an altercation during practice in Bismarck, North Dakota. The center suffered a fractured skull, severe concussion, and a two-centimeter hematoma (bruise) on the left side of his brain. Doctors initially thought it would be months before he could speak, but he was able to within a month, and stated his desire to play basketball within a year. Storey was suspended indefinitely. Days later he had his contract terminated and he was dismissed from the league. Andriuškevičius did not wish to pursue charges.