We present new Spitzer Space Telescope observations of stars in the young ~5 Myr gamma Velorum stellar cluster. Combining optical and 2MASS photometry, we have selected 579 stars as candidate members of the cluster. With the addition of the Spitzer mid-infrared data, we have identified 5 debris disks around A-type stars, and 5-6 debris disks around solar-type stars, indicating that the strong radiation field in the cluster does not completely suppress the production of planetesimals in the disks of cluster members. However, we find some evidence that the frequency of circumstellar primordial disks is lower, and the IR flux excesses are smaller than for disks around stellar populations with similar ages. This could be evidence for a relatively fast dissipation of circumstellar dust by the strong radiation field from the highest mass star(s) in the cluster. Another possibility is that gamma Velorum stellar cluster is slightly older than reported ages and the the low frequency of primordial disks reflects the fast disk dissipation observed at ~5 Myr.