We determine the distribution of circumstellar disk masses in the young (~0.3 Myr) cluster NGC 2024 by imaging a 25 × 25 region in 3 mm continuum emission to an rms noise level of ~0.75 mJy beam^-1 with the Owens Valley Millimeter Array. The mosaic encompasses 147 K-band sources, as well as the molecular ridge seen previously in dust continuum emission. We detect 10 pointlike sources in 3 mm continuum emission above the level of 5 σ within the unit gain region of the mosaic. One of these sources corresponds to the near-IR source IRS 2, an early B-type star. Two other sources are tentatively associated with low-mass near-IR cluster members, and the remaining seven sources have no K-band counterparts. Assuming the millimeter continuum point sources represent emission from circumstellar disks and/or envelopes, then ~6% of the total population (infrared and millimeter sources) in the NGC 2024 mosaic have a circumstellar mass in excess of ~0.06 M. We obtain further constraints on the average circumstellar disk mass by considering the mean millimeter continuum flux observed toward a sample of 140 K-band sources that likely have stellar masses 1-2 M. While none of these sources are detected individually above the 3 σ limit of ~0.035 M, the ensemble of sources are detected in the mean at the 5 σ level with a mean disk mass of ~0.005 M. Compared with the older (~2 Myr) cluster IC 348, NGC 2024 contains a higher frequency of massive disks or envelopes and has a higher mean disk mass by a factor of 2.5 ± 1.3 among K-band sources, suggesting that the mean circumstellar mass is decreasing with cluster age. We also compare the results for the NGC 2024 and IC 348 clusters with those for the lower density Taurus star-forming region. Finally, we compare our detection limits with the minimum mass estimate for the proto-solar nebula and discuss possible implications for planet formation.