A broad continuum excess in the near-infrared, peaking in the rest-frame at 2-5 micron, is detected in a spectroscopic sample of 88 galaxies at 0.5<z<2.0 taken from the Gemini Deep Deep Survey. Line emission from polycyclic aromatic hydrocarbons (PAHs) at 3.3 micron alone cannot explain the excess, which can be fit by a spectral component consisting of a template of PAH emission lines superposed on a modified blackbody of temperature T~850 K. The luminosity of this near-infrared excess emission at 3 micron is found to be correlated with the star formation rate of the galaxy. The origin of the near-infrared excess is explored by examining similar excesses observed locally in massive star forming regions, reflection and planetary nebulae, post-asymptotic giant branch stars and in the galactic cirrus. We also consider the potential contribution from dust heated around low-luminosity active galactic nuclei. We conclude that the most likely explanation for the 2-5 micron excess is the contribution from circumstellar disks around massive young stellar objects seen in the integrated light of high-redshift galaxies. Assuming circumstellar disks extend down to lower masses, as they do in our own Galaxy, the excess emission presents us with an exciting opportunity to measure the formation rate of planetary systems at cosmic epochs before our own solar system formed.