In communication, participants are expected to cooperate through observing a set of maxims. Nevertheless, some communicative instances reveal that there are cases of unintentional non-observance of the maxims, which Grice (1975) categorized as “infringing a maxim”. These instances of infringements call for attention to the extent that they could cause breakdown in communication. In this regard, the aim of this paper is to investigate some cases of infringements of the maxims in selected precautionary inscriptions on some medicine packets, with the objective to examine how such messages are interpreted. The theoretical framework adopted for this research is based on Gricean pragmatics. The method for this research is qualitative and its paradigm is interpretive. The data were collected from some packets of medicine sold in some pharmacy shops in Lagos, Nigeria. One of the major observations made in the course of this research is that, out of the four classes of the Gricean maxims, only the maxim of quality was not infringed in any precautionary inscription in the data. This result may be justified by the reason that precautionary inscriptions on medicine packets should be carefully couched in truth, so as not to jeopardize the health of the patients. Further studies on various cases of infringements in diverse aspects of communication are strongly recommended. Keywords: Precautionary Inscriptions; Communication; Pragmatics; Maxims; Infringements