Interior Minister Mohammad al-Shaar and other top ranking officials escaped unharmed, state television reported.
State news agency SANA said earlier that three bombs struck outside the ministry in the capital's southwestern district of Kfar Sousa, one of them a car bomb.
“Three terrorist explosions, including one caused by a car bomb, struck the interior ministry in Kfar Sousa,” SANA said. “Several people were killed and injured.”
The Syrian Observatory for Human Rights said 25 people were killed and wounded.
Images from the scene broadcast by the pro-government Al-Ikhbariya television channel showed piles of rubble, and blood on the ground.
The adjacent building housing the Egyptian embassy was also hit, Egypt's official MENA news agency reported.
“An embassy employee was injured, and the building was damaged,” MENA quoted Egyptian diplomat Alaa Abdel Aziz as saying.
The Kafar Souseh area of the Syrian capital borders the central Ummayad Square and is contested between rebels and forces loyal to President Bashar al-Assad.
A resident told Reuters she heard sirens and shooting after a “huge explosion.”
Rebels have made gains on the outskirts of Damascus recently but relied on hit and run attacks and bombs in the center of the city, often on state security buildings or areas loyal to Assad, such as Jaramana, where twin bombs killed 34 people in November.
A July 18 bomb attack that killed four of Assad’s closest aides, including his feared brother-in-law Assef Shawkat, was followed shortly by an insurgent advance into the city but they were later pushed back.
At least 40,000 people have been killed in Syria’s uprising, which started in March 2011 with street protests which were met with gunfire by Assad’s security forces, and spiraled into the most enduring and destructive of the Arab uprisings.