The state news agency SANA confirmed the blast in the suburb of Jaramana and said it caused casualties, but did not give a number.
The Britain-based Syrian Observatory for Human Rights said that rebels led by the al-Qaida-linked Jabhat al-Nusra, or Nusra Front, carried out the attack while trying to capture the checkpoint near the town of Mleiha adjoining Jaramana. It reported heavy fighting after the blast.
Rebels control much of the countryside around Damascus but Jaramana, a Christian and Druse area, is mostly loyal to President Bashar Assad. Opposition fighters have previously targeted it with bombings and mortar rounds.
At least 100,000 Syrians have been killed in the country's civil war, now in its third year.