The target set selection (TSS) problem was initially proposed to study the spread of information, ideas, or influence in social networks. It has been used to model many problems arising in various practical applications. In this paper, we study the TSS problem for plane graphs. We provide a characterization of plane graphs $G$ for which $\underset{3}{min}(G)=3$. Consequently, we show that the minimum degree of such plane graphs is at most 4.