We present mid-infrared spectrophotometric results obtained with the ISO on the peculiar X-ray binary Cygnus X-3 in quiescence , at orbital phases 0.83 to 1.04 . The 2.4 - 12 \mu m continuum radiation observed with ISOPHOT-S can be explained by thermal free-free emission in an expanding wind with , above 6.5 \mu m , a possible additional black-body component with temperature T \sim 250 K and radius R \sim 5000 R _ { \odot } at 10 kpc , likely due to thermal emission by circumstellar dust . The observed brightness and continuum spectrum closely match that of the Wolf-Rayet star WR 147 , a WN8+B0.5 binary system , when rescaled at the same 10 kpc distance as Cygnus X-3 . A rough mass loss estimate assuming a WN wind gives \sim 1.2 \times 10 ^ { -4 } { \mathrm { M } } _ { \odot } .yr ^ { -1 } . A line at \sim 4.3 \mu m with a more than 4.3 \sigma detection level , and with a dereddened flux of 126 mJy , is interpreted as the expected He I 3p-3s line at 4.295 \mu m , a prominent line in the WR 147 spectrum . These results are consistent with a Wolf-Rayet-like companion to the compact object in Cyg X-3 of WN8 type , a later type than suggested by earlier works .