"Two mortars launched by terrorists hit the grounds of the Tishreen sports stadium in the Baramkeh district of Damascus, killing a player of Al-Wathba football team and wounding several others during training," the Syrian Arab News Agency said.
The name of the player was not given by SANA, which is widely considered to be the mouthpiece of the current regime.
However, unofficial sources were reported by AFP as saying the player was 26-year-old forward Youssef Sleman, and that he was struck as Al-Wathba and rival team Al-Nawair prepared to leave accommodation adjacent to the stadium for a training session.
"We were collecting our things about to head to the stadium when we heard the first explosion and the windows were blown off,'' Al-Wathba team-mate Ali Ghosn told the Associated Press.
"Youssef was hit in the neck. We ran out to the corridor when the second explosion struck and I saw Youssef fall down bleeding from his neck."
Al-Wathba are from Homs, but were training in Damascus after domestic football resumed this month. The Syrian Premier League had only just restarted after being suspended last summer, with matches played in Damascus in front of empty stands so as to minimise the risk of crowd violence or attacks.
Syria is in a state of civil war, with areas once considered safe now under attack as pro-democracy rebels fight President Bashar Al-Assad’s ruling Ba’ath Party.
Militant Islamists and Kurdish separatists have since entered the equation and, while much of the fighting has been concentrated around Homs and Aleppo, Damascus was relatively safe until recent months.
However, international monitors reported around 50 deaths in Damascus on Tuesday, with around 70,000 estimated to have died in the conflict since it started in 2011.
The national team has been a source of inspiration for Syrian football, winning the West Asian Football Federation Championship at the end of last season and beating Oman in an AFC Asian Cup qualifier this month.