The incident caused a fire which destroyed a doctor's office with an EEG machine and damaged another room.
The identity of the perpetrator who threw the petrol bomb through a window of the hospital's building has not yet been established.
After the attack, graffiti saying "For Successful Treatment" was discovered on the building's wall.
There were no patients in the hospital at the time of the incident, and a doctor on duty called the police and the firefighters.
The hospital's director, Desanka Grubic Jakupcevic, said that the damage could reach several hundred thousand kuna if the EEG was completely destroyed.
She told Hina that it was a special machine which only the Goljak hospital possessed in Croatia.
The director added that the hospital had not received any complaints from possibly dissatisfied parents recently.
A police investigation is under way.