In an important decision, the court also ruled that Russia violated the European Convention on Human Rights by unlawfully detaining the man during a takeover of a Chechen village by Russian troops and by failing to properly investigate the incident.
Fatima Bazorkina filed the complaint against Russia in 2001, after she saw television footage of a Russian officer interrogating her son as troops were taking over the village of Alkhan-Kala. The officer orders soldiers to shoot her son, Khadzhi-Murat Yandiyev, at the end of the footage.
The officer, later identified as Colonel-General Alexander Baranov, was questioned about the incident by Russian authorities but never prosecuted.
The court ruled her son's disappearance caused Bazorkina distress, and also awarded her more than Ђ 12,000 (US$15,100) for court expenses.
Russia has three months to appeal Thursday's verdict, the first in a Chechen disappearance case. Some 200 similar cases are still pending in the Strasbourg court.
Yandiyev was a student at the Moscow Sociology University before going to Chechnya in his final year of studies in 1999 to find his father, who apparently went there, Bazorkina told the court in a hearing last year.