To understand that, you have to remember a few things about Greek philosophy and how it was read by Islamic philosophers.

First, neither Plato or Artistotle were particularly huge fans of democracy, especially Plato whose influence will be huge on thinkers like al-Farabi. Later, Ibn Rushd's (Averroes in western texts) commentary on Plato and Aristotle focused mainly on Plato's Republic, espousing its dislike for democracy, as Aristotle's Politics was notably very hard to get a hold of (Ibn Rushd was THE big promoter of Aristotle). Even then Aristotle was often read through Plato and neo-platonist thought.

Plato's "five regimes" were the main point of reference, from al-Farabi to the Andalucian authors like Ibn Bajja and Ibn Tufayl, up to Ibn Rushd, and that model places democracy second-to-last in a chain of corruption from an ideal enlightened aristocratic government down to tyranny. Reading Plato, your most likely understanding of democracy would be the rule of the mob, which was deeply concerning for most of these thinkers.

Democracy (madina jama'iya) is marked by the freedom of its citizens to do as they please. They are all equal and nobody has mastery over another. Their governor only governs with the explicit consent of the governed. It contains good and bad features "and it is therefore not impossible that at some time the most excellent men (afadil) grow up there, so that philosophers, orators and poets... come into being. It is thus possible to choose from it elements of the ideal state... (therefore) out of democracy most of the ignorant states, good and bad ones together, arise.

• al-Farabi, as quoted in Rosenthal, p.136

Essentially, al-Farabi and Ibn Rushd were a little less pessimistic than Plato and the Andalucian, as they saw democracy as a state not desireable in itself, but which could bring forward the ideal enlightened state (using a bit of Aristotle, mainly Nicomachean Ethics, to distance themselves from the inevitable collapse of democracy into tyranny in Plato).

Now, all that only factors to the extent that Islamic philosophers were not looking for blueprints for political institutions while reading Greek texts. For the most part, they were legal scholars, lawyers, judges, etc., looking for tools and a language to articulate their own concerns (in a pretty similar fashion to how jurists in Medieval Europe would reinvest Roman law, not to replace but to supplement customary law). Thus, the concerns were different, and ideas like Plato's "philosopher-king" (which they would relate to either the Prophet, the Imam or the jurists) resonated much more strongly with them than democracy. There were major differences as to whether the philosophers should actively take part in politics, from al-Farabi who emphasised the identity of the ruler, the scholar, the jurist and the Imam, to the Andalucian who were wary of the masses and the inherent imperfection of politics (a very common theme in Islamic political thought, especially for the Shiah). Their emphasis was much more on reconciling faith and reason, on developing methods to interpret Coranic law.

The most significant Islamic political philosopher, Ibn Khaldun, would later produce something we can consider a "native" political philosophy, less influenced by the Greeks than by the experience of Arab and Turco-Mongol conquests, and the dialectic between nomadic tribes and the sedentary people they conquered. Framed in that way, there's little space for democracy as a political form.

Sources:

• E.I.J Rosenthal, Political Thought in Medieval Islam, An Introductory Outline, Cambridge University Press, 1962

• Majid Fakhry, A History of Islamic Philosophy, Columbia University Press, 2004

Edit: Some formatting plus a slight correction on Ibn Rushd and al-Farabi's slightly more complex take.