Joined at the chest and abdomen with two hearts but one liver, Marek and Michal were separated on September 15 following a 20 hour operation at the Childrens' Faculty Hospital in the Slovak city.
"Marek died this morning at 6.30 (0430 GMT) despite a complex resuscitation and organ support," the hospital said in a statement. Complications set in after the operation with the hospital warning last week that his life hung by a thread.
Michal's condition has not changed and he is still undergoing medical treatment and resuscitation, it added.
He has a chance to survive, according to the hospital's chief doctor, Tibor Sagat, but there are no guarantees concerning his "positive development," Sagat told the Slovak news channel TA3.
The twins mother gave birth in a caesarian operation on April 11.
Seven years ago two conjoined twins were separated sucessfully in Slovakia.