Patat et al. recently inferred the existence of circumstellar material around a normal Type Ia supernova (SN Ia) for the first time, finding time-variable Na I D absorption lines in the spectrum of SN 2006X. We present high-resolution spectroscopy of the bright SN Ia 2007af at three epochs and search for variability in any of the Na D absorption components. Over the time range from 4 days before to 24 days after maximum light, we find that the host-galaxy Na D lines appear to be of interstellar rather than circumstellar origin and do not vary down to the level of 18 mÅ (column density of 2×1011 cm-2). We limit any circumstellar absorption lines to be weaker than ~10 mÅ (6×1010 cm-2). For the case of material distributed in spherically symmetric shells of radius ~1016 cm surrounding the progenitor system, we place an upper limit on the shell mass of ~(3×10-8)/X Msolar, where X is the Na ionization fraction. We also show that SN 2007af is a photometrically and spectroscopically normal SN Ia. Assuming that the variable Na D lines in SN 2006X came from circumstellar matter, we therefore conclude that either there is a preferred geometry for the detection of variable absorption components in SNe Ia, or SN 2007af and SN 2006X had different types of progenitor systems. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. Based in part on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.