US District Judge Florence-Marie Cooper ruled that there was "considerable convincing scientific evidence" that mid-frequency sonar can kill and injure whales and other marine life.
The Navy hopes to use the sonar detect quiet submarines but has been sued over the issue by environmental groups, whose members include actor Pierce Brosnan.
The plaintiffs also include Jean-Michel Cousteau, son of famous French oceanographer Jacques-Yves Cousteau.
Tests on the sonar were scheduled to begin on Wednesday as part of a Navy training exercise that is taking place near the newly established Northwestern Hawaiian Islands Marine National Monument.
The Natural Resources Defence Council and other groups have argued the high-intensity sonar has been shown to damage whales' internal organs, causing them to die at sea or to strand themselves on beaches.
The temporary restraining order will remain in place until July 18th, when a hearing is scheduled on whether it will be extended.
The judge also ordered the Navy and the plaintiffs in the case to meet in order to determine whether the two sides can agree on safeguards to allow the sonar tests to proceed.