The 49-year-old artist, a daughter of Iranian actor Parviz Fannizadeh, died in a hospital in the capital Tehran on Wednesday morning.
The character of Kolah Qermezi was co-created by Iranian actors and directors Iraj Tahmasb and Hamid Jebelli in the 1980s.
Kolah Qermezi is a playful, lazy, kind and sweet character that cannot pronounce words correctly.
For more than two decades, Fannizadeh portrayed Kolah Qermezi, which changed to a cultural phenomenon influencing many Iranians, including children, adults and elderly people.
In addition to Kolah Qermezi, Fannizadeh was the master of several other puppets, including Gorbeyeh Avazeh Khan (Singing Cat) and Khaleh Qourbagheh (Auntie Frog).
The first film featuring Kolah Qermezi, which was released in 1994, is on the list of blockbuster Iranian films.