the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
Muslims should trim their moustaches. The Prophet (peace be upon him) commanded Muslim men to let the beard grow and to trim their mustaches.
Ibn `Umar relates that Allah's Messenger (peace be upon him) said: "To shave the pubic hair, to clip the nails, and to cut the moustaches short, are all characteristics of the natural way (fitrah)." [Sahîh al-Bukhârî (779)]
There is no hard and fast rule about how it should be trimmed. However, it is understood that the it should be trimmed at least so much that it does not extend over the lip.
It is not unlawful to shave it off completely, nor is it especially desirable to do so.
The matter is one wherein there is flexibility.
And Allah knows best.
Source: Islam Today