It is alleged that the two had attempted to undermine the Mass Vaccination Drive through Social Media posts and, by promoting alternative treatments.
Both men were questioned on Saturday and issued with strong warnings.
Police and the Office of the Attorney General will monitor the activities of these and other individuals, and will continue their inquiries.
Law enforcement re-emphasises a caution to members of the public, not to breach the State of Emergency Orders.
Police will monitor any person suspected of breaches in particular, those that prevent the community from being vaccinated or receiving the medical treatment they need.