Zabiullah Mujahid, a Taliban spokesman, said three fighters stormed the building by throwing hand grenades at the guards at the main gate.
Abdul Jabar, a security guard near the building, said the bomber shot two policemen outside the ministry building before entering the large conference hall inside where he blew himself up.
One of the side walls of the building collapsed, while glass littered the roads nearby and office equipment was scattered over the area, a spokesman for the health ministry said.
Hashem Ahelbarra, Al Jazeera's correspondent in Kabul, said: "Eyewitnesses said the suicide bomber apparently made his way to ministry and then blew himself up when inside the offices.
"They have retrieved a number of bodies, but don't have a final death count.
"Police and the security officers have told us to leave the area because they have some concerns that there might be another bomber or bomb inside."