The 64-year-old Ukrainian captain was detained after the crash on the Danube in which at least seven people were killed after the Viking Sigyn, a hotel shop operated by Basel-based Viking River Cruises, crashed into the Hableany sightseeing boat.
The Hableany capsized and sank while the 95-cabin Viking Sigyn "longship" suffered only minor damage.
A total of 35 people were on board the Hableany at the time of the collision. There were seven survivors.
A further 21 people – 19 South Korean tourists and two Hungarian crew members – are still missing with hopes fading they will be found alive.
Hungarian police said they had questioned the captain of the Viking Sigyn as a suspect in relation to “endangering waterborne traffic resulting in multiple deaths”, according to the AFP news agency.
A request for his arrest has now been made, the police statement added.
Police on Thursday night continued to search for possible survivors but the search has been made especially difficult by strong currents after recent heavy rain.
A spokesperson for Viking River Cruises told Swiss news agency Keystone–SDA that no one on board the Swiss vessel had been injured.