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We report the results of the first sensitive L-band (3.4 micron) imaging survey of the young IC 348 cluster in Perseus. In conjunction with previously acquired JHK (1.25, 1.65, 2.2 micron) observations, we use L-band data to obtain a census of the circumstellar disk population to m_K=m_L<=12.0 in the central 110 square arcmin region of the cluster. An analysis of the JHKL colors of 107 sources indicates that 65% +/- 8% of the cluster membership possesses (inner) disks. This fraction is lower than those (86% +/- 8% and 80% +/- 7%) obtained from similar JHKL surveys of the younger NGC 2024 and Trapezium clusters, suggesting that the disk fraction in clusters decreases with cluster age. Sources with circumstellar disks in IC 348 have a median age of 0.9 Myr, while the diskless sources have a median age of 1.4 Myr, for a cluster distance of 320 pc. Although the difference in the median ages between the two populations is only marginally significant, our results suggest that over a timescale of 2 - 3 Myr, more than a third of the disks in the IC 348 cluster disappear. Moreover, we find that at a very high confidence level, the disk fraction is a function of spectral type. All stars earlier than G appear diskless, while stars with spectral types G and later have a disk fraction ranging between 50% - 67%, with the latest type stars having the higher disk fraction. This suggests that the disks around stars with spectral types G and earlier have evolved more rapidly than those with later spectral types. The L-band disk fraction for sources with similar ages in both IC 348 and Taurus is the same, within the errors, suggesting that, at least in clusters with no O stars, the disk lifetime is independent of environment.