The two people killed were Swedish – and a third person was wounded in the attack.
Belgian authorities have raised the terror alert to its highest level in the capital.
“The perpetrator targeted specifically Swedish supporters who were in Brussels to attend a Red Devils soccer match. Two Swedish compatriots passed away. A third person is recovering from severe injuries,” De Croo said.
The shooting took place around 45 minutes before kick-off and three miles (5km) from the stadium.
The score was 1-1 at half-time when the game was suspended and fans were told to remain in the King Baudouin Stadium “until security permits them to leave”.
Fans chanted “All together, All together,” with thousands from both sides also shouting “Sweden, Sweden!” as they waited inside Belgium’s national stadium. The 35,000 supporters were eventually allowed to leave in groups just after midnight local time.
After the game, Sweden coach Janne Andersson confirmed they were told about the incident at half-time and decided not to continue with the match. He said: “Everyone was very sad and all the players agreed not to continue with the match.”
Manchester United and Sweden defender Victor Lindelof said on Instagram: “I’m shocked and devastated by the terrible incidents in Brussels with the cold-hearted attacks on our fellow Swedes.
“I’m lost for words for the cruelty and inhumanity, I want to send my deepest condolences to the families and friends of those affected.
“At the same time, my thoughts go out to all the supporters in Belgium last night, no one should ever go to a game of football and feel unsafe when supporting their team.”
A post from the Swedish FA on the social media platform X, formerly known as Twitter, read: “Keep calm and take care of each other. Our thoughts go out to all the relatives of those affected in Brussels.
The Belgian national FA also wrote: “Our thoughts are with all those affected.”