Soldiers and heavily armed police patrolled the Belgian city on Saturday morning. Streetcar lines that run underground were suspended and the Brussels Metro is due to remain closed until Sunday.
The government has advised people to avoid crowded areas, including shopping centres and concerts.
Some of those who planned and carried out the attacks on the French capital last week lived in Brussels.
Brussels is home to more than 1 million people, as well as the headquarters of the European Union, NATO and a host of international corporations.
Residents were told to avoid gatherings, train stations, airports and commercial districts.
Belgian Prime Minister Charles Michel said that the decision to raise the threat alert to the highest level was "based on quite precise information about the risk of an attack like the one that happened in Paris ... where several individuals with arms and explosives launch actions, perhaps even in several places at the same time."
Speaking at a news conference on Saturday, Mr Michel added: "We urge the public not to give in to panic, to stay calm. We have taken the measures that are necessary."
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The Belgium government will meet again on Sunday to reassess the threat.
Abdelhamid Abaaoud, who is believed to have been the "mastermind" behind the Paris attacks, lived in Belgium's capital. He was killed in a raid on an apartment in the Paris suburb of Saint-Denis on Wednesday.
At least one suspect from the deadly Paris attacks is at large. A manhunt is currently underway to locate Salah Abdeslam, who crossed into Belgium the morning after the attacks.
Last Friday's attacks on the French capital left 130 people dead and dozens injured.
The Bataclan concert hall, bars, restaurants and a football stadium were targeted by Islamic State terrorists.
Of the seven attackers, six are dead. Most of the terrorists had links to France and Belgium.
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The Belgian Federal Prosecutor's office said on Saturday that several weapons were discovered during the search of the home of one of three people arrested in connection with the Paris attacks, but said no explosives were found, the Associated Press reports.
Ahmad Dahman, a 26-year-old Belgian of Moroccan origin, was detained in the Turkey, along with two other suspected Islamic State militants.
Dahmani is believed to have been in contact with the Paris attackers, according to a government official.
This week, France extended a state of emergency for three months, thereby expanding police powers to carry out arrests and searches. It also allows authorities to forbid the movement of persons and vehicles at specific times and places.Suggest a correction