WASHINGTON—A federal judge on Friday ordered the Food and Drug Administration to make the Plan B emergency contraceptive pill available to young teens and girls without a prescription, overturning a 2011 Obama administration decision restricting access to the drug for girls under age 17.

The White House quickly weighed in to say it still believed in its "common-sense" approach even after the judge's ruling. The Justice Department, which is defending the administration's actions in court, indicated it might appeal,...