Clinton was ordered earlier this month by U.S. District Court Judge Emmet G. Sullivan to answer the group's questions under oath. The judge's order was only a partial victory for the group, which had sought to depose Clinton in person.
It was not immediately clear from the wording of Sullivan's order whether Clinton must answer the questions before or after the November election. Judicial Watch contends the deadline is Sept. 29.
Clinton lawyer David Kendall did not immediately respond to an email seeking comment about the timing of his client's planned response. A woman who answered the phone at Sullivan's chambers said he was unavailable to provide clarification.
A law enforcement official also told The Associated Press on Tuesday that the FBI is expected to release documents soon related to its investigation, which focused on whether Clinton and her aides mishandled government secrets.
The official, who wasn't authorized to discuss the matter by name and spoke on condition of anonymity, said documents in the case would be made public as the FBI responds to Freedom of Information Act requests. It wasn't immediately clear when the documents would be released or exactly what they would include.
Though he described Clinton's actions as "extremely careless," FBI Director James Comey said his agents found no evidence that anyone intended to break the law and said "no reasonable prosecutor" would have brought a criminal case.
The FBI this month provided Congress portions of its file from the agency's yearlong investigation.
The FBI interviewed Clinton for several hours at FBI headquarters in Washington just days before announcing its decision to close the investigation. The Justice Department accepted the FBI's recommendation.