Three shells landed in the al-Baramkeh district near the Tishreen Sports Complex where the al-Wathbah team was training at the time, British newspaper The Guardian reported.
The name of the dead player was not reported.
The Syrian state news agency Sana blamed opposition fighters for the attack.
The rebel Free Syrian Army claimed responsibility for an attack Tuesday in the capital's northwestern Muhajireen district, The Guardian said. Two mortars exploded near Tishreen palace, one of Bashar Assad's presidential palaces.
The Syrian Network for Human Rights reported 97 deaths in the country Tuesday, most of them in Aleppo and Damascus.
Meanwhile, rebel commanders say arms shipments from outside Syria have slowed, prolonging the nearly two-year conflict, the Los Angeles Times reported.
The rebel army is blaming the slowdown on the United States, which they say is putting pressure on its allies in the Persian Gulf region, that are largely responsible for the arms supplies.