The explosion ripped through the courtroom in Jibla, 125 miles south of the Yemeni capital of San'a, at 8:50 local time (1:50 ET), police said, speaking on condition of anonymity.
Police said a judge was injured. Witnesses said they saw victims being taken away in ambulances.
Officials did not promptly give a figure for the number of casualties. It was not immediately clear if anybody had been killed.
Police said they had detained a man in connection with the explosion. He was arrested in the yard of the courthouse.
On Saturday, the court condemned to death Abed Abdul Razak Kamel, 30, after convicting him of the Dec. 30 shooting deaths of Kathleen A. Gariety of Wauwatosa, Wis., Martha C. Myers of Montgomery, Ala., and William E. Koehn of Kansas. The killings took place at the Southern Baptist-run hospital in Jibla.
The judge injured Wednesday was not the one who sentenced Kamel.
Yemeni security officials have said they believe Kamel belonged to a terrorist cell linked to al Qaeda.
Kamel testified that on the day of the shootings, he walked into the hospital with a semiautomatic rifle hidden under his clothes and opened fire on a staff meeting involving the Americans, firing two shots at each target.
He told the court he killed the missionaries "out of a religious duty … and in revenge from those who converted Muslims from their religion and made them unbelievers."
Security officials surrounded the court building Wednesday and cordoned it off.
Yemeni security officials have said audiotapes bearing the voice of al Qaeda leader Osama bin Laden had been found at Kamel's house. Police said they believed Kamel was part of a group that was plotting attacks against at least eight targets, including foreigners and Yemeni politicians.
Bin Laden was born in Saudi Arabia, but his family comes from Yemen. U.S. officials believe a number of terrorist attacks in Yemen, notably the bombing of the destroyer USS Cole in Aden harbor in 2000, were carried out by al Qaeda.
Yemen, a country of 18.7 million people that is about twice the size of Wyoming according to the CIA, supports the U.S. campaign against terror.
In late March, the State Department allowed non-emergency personnel and diplomats' adult family members to leave Yemen if they wished, warning of "credible reports that terrorists have planned attacks against U.S. interests" there. Diplomats have been barred from brining their kids to Yemen since March of 2002.