Explosions at Zaventem Airport and Maelbeek metro station in the Belgian capital killed 26 people and injured 136, according to the latest official figures.
The Royal Belgium Football Association (KBVB-URBSFA) announced the cancellation of a scheduled national team training session in the wake of the news.
Kompany is not part of Marc Wilmots' squad, who face Portugal in Brussels on Friday, due to a calf injury sustained during Manchester City's Champions League match against Dynamo Kiev last week.
The 29-year-old, who was born in the Brussels municipality of Uccle, tweeted: "Horrified and revolted. Innocent people paying the price again. My thoughts are with the families of the victims.
"I wish for Brussels to act with dignity. We are all hurting, yet we must reject hate and its preachers. As hard as it may be."
Kompany previously addressed the issues of radicalisation and terrorism in a wide-ranging interview with CNN following the Paris terror attacks after it emerged the suspected ringleader of coordinated assaults that killed 130 in the French capital, Abdelhamid Abaaoud, grew up in the Brussels district of Molenbeek.
"There's a sense of me that really believes that it was predictable, really predictable," he said.
"I think it was inevitable, because I only used to see politicians in our neighbourhoods once every six years when they needed to come for votes.
"Now and then something would pop up out of the ground and somebody would cut a red ribbon to say that we've done this for the community.
"But I have really struggled to see a real concern, a genuine desire to be a part of making those neighbourhoods.
"The reason why [the Paris attacks] hurt me so much is because they're not people of a religious faction, they're people that have been able to fall off the grid and people have been able to indoctrinate them."
Norwich City issued a statement confirming their striker Dieumerci Mbokani was "unharmed but shaken" having been at Zaventem Airport during the explosions.