The request follows a similar order last year, to which YouTube complied. Clips of Viacom-owned shows such as The Daily Show have crept back on to the site.
Viacom said: "Filtering tools promised repeatedly by YouTube and Google have not been put in place. It continues to host vast amounts of unauthorised content."
Viacom claims the missed revenue opportunity is as much as $48 million, based on ads on Comedycentral.com.
A YouTube spokesman said: "We have received a DMCA takedown request from Viacom and we will comply with it. We take copyright issues very seriously. We prohibit users from uploading infringing material."