The court sided with Marzet Imakayeva, a Chechen woman who fled Russia to seek asylum in the United States two years ago.
Imakayeva's son disappeared after being detained in 2000, and her husband disappeared two years later. Imakayeva said authorities were responsible for both men's disappearance and presumed death.
The court awarded the applicant 90,000 euros (over $114,000) in damages. Russia has three months to appeal the ruling.
The ruling is the third in four months against Russia in cases concerning the Chechen war.