WASHINGTON — The wife of an American man secretly detained in Yemen for more than a year said in a Facebook posting that her husband was being held “unjustly” by one of the country’s security agencies and expressed disappointment that the United States government has been unable to free him.

Jihan Mohamed said her husband, Wallead Yusuf Pitts Luqman, was abducted in April 2015.

This is the first time that Mr. Luqman has been publicly identified as being held by the Houthis, a Shiite rebel group, in Yemen. The family had stayed silent for fear that public discussion of his kidnapping could endanger his life.

Ms. Mohamed said late Thursday on Facebook that her husband was arrested while trying to leave Yemen. The family was on a bus headed for Saudi Arabia when he was taken.