The proceeding took place at Weill Cornell Medical Center in Manhattan, where Ortega has been held.
Cloaked in a hospital blanket and handcuffed to a bed, she did not speak. Her attorney, Valerie Van Leer-Greenberg, entered the plea on her behalf.
Her next court date is scheduled for January 16, following a psychological evaluation, authorities said.
"This crime shocked and horrified parents around the city, many of whom entrust their children to the care of others both by necessity and by choice," Manhattan District Attorney Cyrus R. Vance said in a statement.
"My heart goes out to the family of those beautiful young children, and I hope that, with time, this family will heal."
Ortega, 50, was arrested last month and accused of stabbing Lucia Krim, 6, and her brother Leo, 2.
She was later indicted on first- and second-degree murder charges in both deaths.
Police say that on October 25, the children's mother, Marina Krim, returned to the family's Manhattan apartment, found Lucia and Leo dead in the bathroom and saw the nanny stab herself with a kitchen knife.
A native of the Dominican Republic, Ortega had been a naturalized U.S. citizen for 10 years.