The Cameroonian was stretchered off during the 1-1 draw with Ross County in Dingwall and will miss seven to eight months of football.
Following Friday's revelation that Jamie Brandon is out until near Christmas, it is a disastrous double whammy for the Tynecastle club. Djoum is likely to need surgery on the problem before beginning a rehabilitation programme.
He fell innocuously after chesting the ball down in midfield during the first half of Saturday's match. A stretcher was quickly called for, with news confirmed later that his Achilles had snapped.
The 28-year-old previously missed almost three months in total this season with two knee injuries. His latest problem, however, is considerably more serious and comes straight after the Brandon news.
The teenage defender has a ruptured anterior cruciate ligament (ACL) plus a torn meniscus tendon and is expected to be sidelined for up to nine months.