We determine the distribution of circumstellar disk masses in the young ( \sim 0.3 Myr ) cluster NGC 2024 by imaging a 2 \hbox to 0.0 pt { . } ^ { \prime } 5 \times 2 \hbox to 0.0 pt { . } ^ { \prime } 5 region in \lambda 3mm continuum emission to an RMS noise level of \sim 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 point-like sources in \lambda 3mm continuum emission above the level of 5 \sigma 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 7 sources have no K-band counterparts . Assuming the millimeter continuum point sources represent emission from circumstellar disks and/or envelopes , then \sim 6 \% of the total population ( infrared and millimeter sources ) in the NGC 2024 mosaic has a circumstellar mass in excess of \sim 0.06 M _ { \odot } . 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 \lesssim 1 - 2 M _ { \odot } . While none of these sources are detected individually above the 3 \sigma limit of \sim 0.035 M _ { \odot } , the ensemble of sources are detected in the mean at the 5 \sigma level with a mean disk mass of \sim 0.005 M _ { \odot } . Compared to the older ( \sim 2 Myr ) cluster IC 348 , NGC 2024 contains a higher frequency of massive disks/envelopes and has a higher mean disk mass by a factor of 2.5 \pm 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 to 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 .