A jury found Drew guilty in November of three misdemeanor counts of accessing computers without authorization.
Prosecutors said Drew violated the rules by helping create a fictitious 16-year-old boy on MySpace and sent flirtatious messages from him to teenage neighbor Megan Meier.
The "boy" then dumped Megan in a message telling her "the world would be a better place without you."
Megan hanged herself soon afterward in her bedroom closet in October 2006.
In his dismissal motion, attorney Dean Steward argued that prosecutors failed to show a crime was committed because his client violated MySpace service terms.
"Put simply, the question is this: Is it a federal crime to violate a Web site terms of service?" Steward wrote. "The correct answer should be a resounding no."
Jurors found Drew was not guilty of the more serious felonies of intentionally causing emotional harm and couldn't reach a unanimous verdict on a felony conspiracy charge.
Prosecutors want Wu to dismiss the conspiracy charge "in the interests of justice," according to court documents. An e-mail message left for prosecutors wasn't returned.
The case hinged on an unprecedented application of computer-fraud law. Drew was not directly charged with causing Megan's death, but she was indicted under the federal Computer Fraud and Abuse Act, which in the past has been used in hacking and trademark theft cases.
Drew faces up to three years in prison and a $300,000 fine. The trial was held in Los Angeles because the servers of the social networking site are in the area.