Phuket Provincial Police Commander Choti Chavalviwat said Mr Kvalka might be transferred to Phuket today, where the investigation would continue.
Mr Kvalka is one of two suspects in the murder case. The other man, Mr David, police say confessed to the murder of Hungarian Mr Reisz on Thursday, after being arrested in Bangkok. Yesterday he re-enacted out the events at the crime scene.
Mr Kvalka had evaded police capture until now.
The body of Mr Reisz was found last Friday (November 30) in Patong. He had been stabbed multiple times and bashed in the head, and dumped, wrapped in plastic. The police believe he was murdered on November 24.