Col. Tara Osborn also said Maj. Nidal Malik Hasan will be tried in Texas, rejecting a defense request to move his court-martial, the Los Angeles Times reported.
Osborn's ruling on a guilty plea repeats the one made by the previous judge in the case, Col. Gregory Gross. Both said military law bars guilty pleas in capital cases.
Hasan faces 13 counts of premeditated murder and 32 of attempted murder for the 2009 massacre at Fort Hood. He was allegedly inspired by Anwar Awlaki, a U.S. citizen who became a leader of al-Qaida in the Arabian Peninsula and was killed by a U.S. drone.
Osborn said the trial will begin July 1 with selection of a military jury starting May 29.
Hasan, 39, the son of Palestinian immigrants, spent eight years as an Army enlisted man. After graduating from college, he was accepted at the Uniformed Services University of the Health Sciences.
Before his transfer to Fort Hood, he spent eight years at Walter Reed Army Medical Center in Washington.
Hasan faces the death penalty or life with no parole if he is convicted.