The SNR52 gene, coding for a box C/D snoRNA, is the only snoRNA gene transcribed by RNA polymerase (Pol) III in Saccharomyces cerevisiae. Pol III transcription generates a precisely terminated primary transcript that undergoes extensive 5′-end processing. Here, we show that mutations of the box C/D core motif required for snoRNP assembly compromise 5′-end maturation of the SNR52 snoRNA. Upstream processing was also impaired by specific depletion of either Nop1p or Nop58p snoRNP proteins. We further show that the nuclear exosome is required for 3′-end maturation of SNR52 snoRNA, at variance with all the other known Pol III transcripts. Our data suggest a functional coupling between snoRNP assembly and 5′-end maturation of independently transcribed box C/D snoRNAs.