Earlier, the Canucks dealt their lone second-round pick (No. 60) to the Minnesota Wild in exchange for the 71st and 101st overall picks.
Honzik, a 17-year-old Czech, spent last season with the Victoriaville Tigres of the Quebec Major Junior Hockey League. He had a record of 17-12-1 and a goals-against average of 3.54.
The Canucks selected Quebec Remparts forward Alexandre Grenier with the No. 90 pick and grabbed Minnesota high-school forward Joseph Labate at No. 101.
Vancouver selected Swedish defenceman Nicklas Blomstrand with the No. 120 pick and took Sudbury Wolves defenceman Frank Corrado at No. 150.
The Canucks took two more Swedish players with their final two picks. Malmo forward Pathrik Westerholm was selected at No. 180 and Frolunda defenceman Henrik Tommernas was picked at No. 210.
On Friday night, the Canucks used their first-round pick to select Oshawa Generals forward Nicklas Jensen at No. 29.