Belgian media said the blast was caused by a car which rammed the building.
It comes as Belgium remains on high alert following the devastating Islamic State-claimed suicide attacks on the city's airport and metro in March.
"There was no one at the site" in the northern Brussels suburb of Neder-Over-Heembeek, a spokesman for the prosecutor's office told AFP, refusing to comment on the cause except to say the explosion had a "criminal origin".
The prosecutor has set up a "crisis centre", the spokesman said.
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"The explosion was extremely powerful," said Meys. "Windows of the lab were blown out dozens of metres away."
He said about 30 firefighters were at the scene at around 3:00am fighting the blaze.
RTBF television said two suspects rammed a car into the institute grounds and threw an incendiary device at it.
The institute is part of Belgium's federal justice system.
Among its tasks is to carry out scientific analyses linked to criminal cases and to study the functioning of the penal system.
Belgium has been high alert after suicide bombers struck Brussels airport and a metro station near the European Union headquarters on March 22, killing 32 people.
The jihadist cell responsible for the Brussels attacks was also heavily involved in the November Paris attacks in which 130 people were killed and hundreds more wounded.
The bombmaker for the Paris attacks, Najim Laachraoui, blew himself up at Brussels airport.
Earlier this month it emerged that Belgian authorities were also hunting a cousin of the El Bakraoui brothers who also blew themselves up in the Brussels attacks.
Belgium has caught several people linked to the Brussels and Paris atrocities including Salah Abdeslam, the last surviving member of the Paris IS cell, who has since been extradited to France.
Abrini has not yet been handed over pending further investigation into the Brussels attacks.