The pensioner had taken the call to "Fill it!" on the piece by artist Arthur Koepcke too literally and damaged the artwork, Eva Martin said.
It should normally be clear to all visitors that they were not allowed to scribble on works on display, the spokeswoman added.
Koepcke (1928-1977) is part of the Fluxus art movement which experiments with different media and disciplines.
The damaged work, which has an insurance value of 80,000 euros, is due to be restored, according to the museum.
Meanwhile, police are investigating the crossword puzzle-loving pensioner, who is reported to have been surprised by the museum's complaints against her.
- DPA