One circumstance that would allow arrest is if the ship's flag is that of a country that has signed the Rome Statute. Then, you can be arrested immediately, as the law of that country applies on the ship. The captain has the right (if not even duty) to detain you.
As an example, the swiss law on high sea shipping (Seeschifffahrtsgesetz) states in Art 1:
Die Seeschifffahrt unter der Schweizer Flagge4 untersteht dem schweizerischen Recht, soweit dies mit den Grundsätzen des Völkerrechts vereinbar ist.
The shipping under Swiss flag is under Swiss Law, asfar as this is possible under public international law.
Later on, the law states that the captain has the power of the Police to investigate a crime on board the vessel or to detain a suspect. The law doesn't explicitly state that he has to execute an arrest warrant on a passenger, but I would guess that's just because that law isn't supposed to include all possible cases.
Other countries for certain have similar regulations, as this is one of the reasons ships must fly a flag. Most civil and criminal issues (except typically for customs issues, when the ship is in foreign ports) are handled according to that country's law.