Charles Michel described the capture of French suspect Salah Abdeslam, aged 26, and two others as “a very important result in the battle for democracy”.
French president François Hollande said he was confident they had links to Syria and to Islamic State, which claimed responsibility for the attacks that killed 130 people.
“The threat level is very high,” said Mr Hollande, who was in Brussels for an EU summit.
He added that it was now clear many more people had been involved in the Paris attacks on a sports stadium, bars, cafes, and concert hall than had been realised.
Mr Michel said Abdeslam was wounded — local media said he was shot in the leg — in the operation launched as EU leaders met on the other side of the city to discuss Europe’s migration crisis. US president Barack Obama sent his congratulations.
Television footage showed armed security forces dragging a man with a sack on his head out of a building and into a car.
“We got him,” Belgian government minister Theo Francken said on Twitter.
Mr Hollande said France wanted to extradite Abdeslam, who was born and raised in Brussels to a Moroccan immigrant family, and hoped he would yield more clarity about an operation mounted by Syrian-based Islamic State, in which all the known attackers died.
Several bursts of gunfire rang out earlier in the capital’s Molenbeek area — Abdeslam’s home neighbourhood and the scene of past investigations into the Paris attacks — and police officers surrounded an apartment block there from around 4pm local time.
Two explosions were heard after the arrest, though it was unclear whether they were part of a new operation or a clear-up. Some four hours later, the main police presence had stood down but crime scene investigators were still at work.
Some 130 people were killed in the terrorist attacks on Paris on November 13 as militants attacked customers at bars and cafes, and music fans at a concert by American rock group Eagles of Death Metal.