The Australian bank's Macquarie Infrastructure and Real Assets (MIRA) arm did not disclose the financial terms of the deal in its emailed statement to Reuters.
MIRA acquired its initial stake in Brussels Airport as part of the airport's privatisation in 2004. The sale is expected to be completed by year-end, it said.
JPMorgan, Shearman & Sterling and Baker McKenzie advised MIRA on the sale.
(Reporting by Sathvik N in Bengaluru, editing by G Crosse)