The judge, Army Col. Denise Lind, ruled two dozen witnesses will be allowed to give at least some of their testimony in secrecy, The Washington Post reported. Lind said alternatives, such as using code names, were considered to keep the entire trial open, but ultimately she decided that would allow people to "connect the dots" and learn classified information, the newspaper said.
Manning's trial at Fort Meade, Md., is scheduled to start June 3. About 150 witnesses are expected to be called during the court-martial, which is expected to take three to four months.
Manning is charged with leaking more than 700,000 government and military documents to the whistle-blower group WikiLeaks.
The former intelligence analyst pleaded guilty to several counts in February, but still faces others, including aiding the enemy and violating the Espionage Act.
Prosecutors said Tuesday they will not to pursue a charge alleging he violated the federal Computer Fraud and Abuse Act. The Post said prosecutors didn't say why they were dropping that charge.
Manning could still face life in prison if convicted on the more serious charges against him.
Lind also dealt the defense a setback by ruling prosecutors can call witnesses concerning any damage caused by WikiLeaks' release of documents to provide context and evidence of damage. Lind said, however, she would impose limits so the trial would not "devolve into many trials regarding international politics in many regions of the world."