The grassroots network Local Co-ordination Committee said the rocket hit a building, but it put the death toll much higher, at 54 dead, including several children.
Footage of the blast on YouTube showed a crowd of men pulling the bloodied body of a young girl from the rubble.
An activist who asked not to be named said the blast may have been an explosion from inside the building.
Hama, a centre of revolt in the uprising against President Bashar al-Assad's rule, has a small team of UN observers, who are preparing the way for a larger UN mission, which will monitor the peace plan brokered two weeks ago by the UN-Arab League envoy Kofi Annan.
Separately, Syrian forces shot dead four civilians on a bus, and fighting raged near Damascus, dissidents said.
France said the UN should consider harsher measures if the international peace plan, which has been shaken by violence, ultimately collapses.
The French foreign minister, Alain Juppé, said Paris would push for a Chapter 7 UN resolution, which would mean punitive sanctions, next month if Assad's forces did not pull back.
"This cannot continue indefinitely. We want to see observers in sufficient numbers, at least 300 … deployed as quickly as possible," Juppé said.
"If that does not work, we cannot allow the regime to defy us. We would have to move to a new stage with a Chapter 7 resolution at the United Nations to take a new step to stop this tragedy."
