The suspect in the attack was shot by two of the officer's colleagues and has also been hospitalised in a "critical condition"
The stabbing came during a state visit to Belgium by French President Emmanuel Macron that has revived memories of the Paris and Brussels attacks.
Brussels prosecutors said an investigating magistrate will open an inquiry into possible "attempted murder in a terrorist contact" but that a motive had not been established.
Federal prosecutors, who would oversee a terrorist case, have not yet joined the investigation.
Three dead in suspected 'terror' shooting in Belgian city
"The suspect had several kitchen knives in his hands and stabbed the officer several times," the prosecutor's office said, adding that the officer had been treated for a neck wound and was expected to survive.
"The inquiry will determine if this was a terrorist act," it added.
Earlier, Belgian Interior Minister Jan Jambon said, "a priori", the suspect in the "cowardly attack" was not listed in Belgium's counter-terrorism database.
The assailant stabbed the officer outside the central police station in Brussels' historic city centre at 5:30 am (0430 GMT), police spokeswoman Ilse van de Keere told AFP.
Despite the incident, Macron later visited a cultural centre around a kilometre (under a mile) away in Molenbeek, home of some of the who carried out the 2015 Paris attacks that left 130 people dead.
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