The paper presents an interactive module created through the Wolfram Demonstrations Project that visualizes the Zeeman effect for the small magnetic field strengths present in the interstellar medium. The paper provides an overview of spectral lines and a few examples of strong and weak Zeeman splitting before discussing the module in depth. Student discovery is aided with example situations to investigate using the interactive module, which is targeted at the upper undergraduate or early graduate level. This module (http://demonstrations.wolfram.com/ TheZeemanEffectInTheInterstellarMedium), which uses free software, can be used in classroom activities or as a means of introducing students to the Wolfram Demonstrations Project as a learning resource.