Both sides needed a victory to put just the slightest pressure on runaway leaders PSV, who now have a six-point advantage over champions Ajax and 14 points over third-placed Feyenoord.
It was only the second time the great 'Klassieker' fixture of the Dutch season had ended in a goalless draw. The previous time was in 1978.
Feyenoord dominated proceedings at the home of the team who are seeking a record fifth successive title and had two good chances in the first half.
Colin Kazim-Richards shot wide and then Jean-Paul Boetius has his shot cleared off the line by Ajax striker Arkadiusz Milik.