Yes, technically you can arrest a vessel. That is what it is, and has been, for the past couple of hundred years.
The arrest warrant is issued, by a court, then depending on the jurisdiction, a lawyer or bailiff must climb aboard, and arrest the vessel to prevent it leaving the territorial waters of the country where it is under arrest. In some jurisdictions, a company can pay a bond to cover the claim against its vessel to have it released while the court case proceeds. Legally, it is probably the most fascinating area of maritime law, and that's not even getting to sister-ship arrests.
But I'm really not sure how your comment about Miranda rights has anything to do with the arrest of a vessel.