The Administrative Court of Cundinamarca set a three-month deadline for the Ministry of Environment to issue "a regulation that contemplates measures for the eradication of the species," which is affecting the area's "ecological balance."
In their homeland in Africa, the animals are responsible for more human deaths than almost any other animal, but in Colombia, the hippopotami have become loved members of the local community and a tourist attraction.
They've also been increasingly posing problems for the local community near Escobar's old ranch in Antioquia state -- one that experts worry may soon turn deadly.
After Escobar's death, hippos from his private zoo made their way into nature, in an area of abundant vegetation and where there are no predators.
There are now some 166 of the two-ton beasts wandering freely.
Attacks on fishermen have been reported on the Magdalena River, and experts argue manatee populations could be threatened -- though animal rights activists and tourism workers oppose hippopotamus hunting.
The court specified that measures to eliminate the hippos should include "controlled hunting and sterilization."
The environmental ministry had already announced last year plans to sterilize part of the population, while euthanizing others, as part of an effort to contain the growing number of hippos.
The sterilizations have proceeded slowly while no cases of euthanasia have been carried out.
Plans to move the animals to Mexico, India or the Philippines have also floundered.