He described Brandon as "a woman with an excellent curriculum vitae".
The shooting took place in late morning on Thursday in a building 100 metres from the Palace of Justice in the centre of the capital.
"A person entered the tribunal, remained there some time, then killed, at close range, before fleeing," said De Clerck.
"We are searching for this person," and there were witnesses, the minister said.
Jean-Marc Meilleur, a spokesman for the Brussels prosecutor's office, said the man had been "present at the outset of the hearing".
"Toward the end of the session, he pulled a gun. Shots were fired, after which the killer fled," he said.
Meilleur told a news conference "the gunman did not speak".
Speaking to Al Jazeera from near the scene in Brussels, Terri Schultz, a reporter, said: "This man is still on the loose and that really is troubling the lawyers and employees of this district.
"Some of them are afraid to go back in the building, some are afraid to go back in the street."
Schultz said the magistrate was shot at point blank range and that a witness had followed the man as he ran down the street but was unable to catch up with him.
Belgian media identified the dead clerk as Andre Bellemans.
Security at court buildings in Belgium has been found wanting on several occasions in recent years, including spectacular criminal escapes from the palace.