This paper discusses evidence for and properties of disks associated to brown dwarfs in the star-forming region \rho~ { } Oph . We selected nine objects from the ISOCAM survey of Bontemps et al . [ 2001 ] that have detections in the two mid-infrared bands ( 6.7 and 14.3 \mu m ) , relatively low extinction and low luminosity . We present low-resolution near-infrared spectra in the J , H and K bands , and determine for each source spectral type , extinction , effective temperature and luminosity by comparing the spectra to those of field dwarfs and to the most recent model stellar atmospheres . The results indicate that eight objects have spectral types M6–M7.5 , effective temperature of 2600–2700 K , one has a later spectral type ( M8.5 ) and lower temperature ( about 2400 K ) . The derived extinctions range between A _ { V } \sim 2 and 8 mag . The location of the objects on the HR diagram , in spite of the uncertainties of the evolutionary tracks for young objects of substellar mass , indicates that all the objects are very young and have masses below about 0.08 M _ { \odot } . The coolest object in our sample has mass in the range 8-12 M _ { J } ( 0.008–0.012 M _ { \odot } ) . In all cases , the mid-infrared excess is consistent with the predictions of models of disks irradiated by the central object , showing that circumstellar disks are commonly associated to young brown dwarfs and planetary-mass objects . Finally , we discuss possible variations of the disk geometry among different objects , as well as the possibility of using these data to discriminate between various formation scenarios .