V838 Monocerotis had an intriguing, nova-like outburst in January 2002 which has subsequently led to several studies of the object. It is now recognized that the outburst of V838 Mon and its evolution are different from that of a classical nova or other classes of well-known eruptive variables. V838 Mon, along with two other objects that have analogous properties, appears to comprise a new class of eruptive variables. There are limited infrared studies of V838 Mon. Here, we present near-infrared H band (1.5 - 1.75micron) spectra of V838 Mon from late 2002 to the end of 2004. The principal, new result from our work is the detection of several, rotation-vibration lines of water in the H band spectra. The observed water lines have been modeled to first establish that they are indeed due to water. Subsequently the temperature and column densities of the absorbing material, from where the water absorption features originate, are derived. From our analysis, we find that the water features arise from a cool ~750-900 K region around V838 Mon which appears to be gradually cooling with time.