The Zaventem facility has been closed since a twin suicide bomb attack on the departures hall on 22 March.
The SLFP police union told the BBC that security measures put in place for the reopening were insufficient.
So-called Islamic State (IS) said it carried out bombings of the airport and metro system that killed 32 people.
Vincent Gilles, the president of the SLFP, the largest police union in Belgium, said: “We are on strike because of what happened on 22 March – we cannot continue as if this day has not happened.
“The police feel the security measures put in place by the airport company are insufficient for those who work and use the airport.”
He says metal detectors, body scanners and x-ray machines should be set up to screen people before they are allowed into terminals.
The authorities have so far rejected this, arguing that such checks would create new queues outside the buildings, leading to fresh security risks.
In an earlier statement, the airport’s operators had said a partial reopening would be possible on Friday evening, after a temporary check-in system had been tested and made ready.
However, it said the departures area, which was severely damaged by the bomb attacks, would only operate at 20% of normal capacity, receiving only 800 departing passengers per hour.
The operator said on Friday this could not now go ahead because of the strike. Belgian media said the government was still considering the possibility of a reopening.
Defence Minister Steven Vandeput said: “We must find a balance between economic needs and security needs.”
The airport operator’s chief executive, Arnaud Feist, said earlier this week that the airport would take months to reopen fully.
In an earlier open letter to authorities published by Belgian broadcaster VRT (in Dutch), police had said they had sent “strong daily signals regarding the overall security at the airport”.
They also alleged that too many airport employees had criminal backgrounds.
Police are still searching for the third man who took part in the airport attacks. The man, pictured on CCTV wearing a hat, was said to have fled the scene without detonating his explosive device.
The two airport bombers who died have been named as Najim Laachraoui and Ibrahim el-Bakraoui.
Bakraoui’s brother, Khalid el-Bakraoui, blew himself up at Maelbeek metro station.
Police later found a computer in which Ibrahim el-Bakraoui left a final message.
The BBC has learned that the same computer contained plans and photos of Prime Minister Charles Michel’s office and home.
Also on Friday, an Italian court approved the extradition of Djamal Eddine Ouali, an Algerian national accused of forging identity documents for those involved in the Brussels bombings and in the Paris attacks that killed 130 people in November.
Mr Ouali, 40, was arrested last weekend in the southern Italian city of Salerno. The court said he would be sent to Belgium within 10 says. His lawyer said he would appeal.