Anzac Day originally commemorated a battle on the Gallipoli peninsula in Turkey during World War One
The boat was carrying two sailors and 20 passengers when the collision occurred in waters near Incheon west of Seoul, a coast guard official told a media briefing.
Two people remain missing and a search and rescue operation involving five helicopters and 19 vessels is underway.
President Moon Jae-in ordered all measures be taken to find those missing, his office told reporters.
Those rescued from the water have been sent to nearby hospitals, the coast guard said.
The reason for the collision has yet to be confirmed, according to the coast guard.