Some of the Morrowind MQ has level requirements for the quests, but they are usually pretty low and your character will easily be higher than the required level just by progressing through the quests.
The level you're at when you finish any of the three MQ's depends on how you played them, and when you started them.
At least 20. Tribunal is for high-level characters.
At least 25. It's even more difficult then Tribunal.