The complaint, filed by the Missouri branch of the American Civil Liberties Union (ACLU), asks the court to grant an injunction permitting the juror to speak out. "In plaintiff's view, the current information available about the grand jurors' views is not entirely accurate," the lawsuit says.
Mr McCulloch, the St Louis county prosecutor, is named as the defendant as he would be responsible for charging a grand juror who spoke without a court's permission. The suit alleges he presented evidence in a "muddled" and "untimely" fashion.
Missouri governor Jay Nixon was criticised before the grand jury decision for not appointing a special prosecutor to oversee the case in place of Mr McCulloch, whose father, a police officer, was shot dead on duty.
The grand jury, which was made up of nine white and three black people, needed nine of its 12 votes in order to charge Mr Wilson with a crime. The process was abnormal in both its duration and the depth of evidence presented: the jurors met on 25 days over three months, and heard more than 70 hours of testimony from some 60 witnesses. After the panel made its decision, Mr McCulloch published much of the evidence it had seen.
Grand Juror Doe's lawyers said the gag order ought to be lifted given the case's uniquely high profile. The juror is eager to "contribute to the current public dialogue concerning race relations", the suit said.
"Right now there are only 12 people who can't talk about the evidence," ACLU lawyer Tony Rothert said.
"The people who know the most... are sworn to secrecy. What (the grand juror) wants is to be able to be part of the conversation."