Summary: A set \(C\) of vertices of a simple graph is called a completely regular code if for each \(i = 0, 1, 2, \dots\) and \(j = i - 1, i, i + 1\), all vertices at distance \(i\) from \(C\) have the same number \(s_{ij}\) of neighbors at distance \(j\) from \(C\). We characterize the completely regular codes in the infinite hexagonal grid graph.