Brobbey was forced off after 35 minutes of Thursday's UEFA Nations League meeting with Germany.
Xavi confirmed after the match that the striker would not feature again during the international window and that a replacement would be called up.
The KNVB confirmed on Friday that Zirkzee had been selected to fill the vacant spot.
It is Zirkzee's first Netherlands call-up since Euro 2024, when he made brief appearances against England and Turkey. He has now been handed another opportunity to make an impact for Oranje as they continue their Nations League campaign.
The Manchester United striker has had limited opportunities at club level this season, playing just 20 Premier League minutes. His appearances have come as a late substitute against Manchester City and Fulham.
Zirkzee could now feature when the Netherlands travel to Belgrade to face Serbia on Sunday.
Oranje will then travel to Greece before completing the international break against Serbia in Eindhoven.
Erling Haaland made history with a two-goal display as Norway beat Denmark 3-2 in the Nations League, taking him past Zlatan Ibrahimovic as the highest-scoring Nordic men's international player.
Jurgen Klopp was left encouraged by Germany's performance in his first match as head coach, despite seeing his side concede a late equaliser in a 1-1 draw with the Netherlands in the UEFA Nations League on Thursday.
Liverpool defender Virgil van Dijk believes the Netherlands can make significant progress under new head coach Xavi Hernandez after beginning his tenure with a 1-1 draw against Germany.
Leeds United star Ethan Ampadu has demanded greater standards from Wales after their winless run was extended by a 1-0 Nations League loss to Portugal in Lisbon.
