The Dutch international suffered the problem, which is likely to rule him out for the majority of the season, during last week's Capital One Cup tie away at Swindon Town.
Having suffered the same injury as the 20-year-old on two separate occasions, Essien has moved to reassure his fellow midfielder that he will return soon.
"I would like to wish Marco van Ginkel all the best with his injury and recovery. Having suffered two cruciate ligament injuries myself, I know how it feels and the hard work that lies ahead of him," he told the club's official website. "He is young so I expect him to come back sooner than expected. All the best Marco."
Van Ginkel joined Chelsea in the summer from Vitesse Arnhem.