There are two views about this. The Hanafiyah and the Hanbaliyah view it as sunnah to shave it off. The MAlikiyah and the Shafi'iyah view it that it is sunnah to trim the moustache not shave it, and shaving it is makrooh.
The Standing Committee for Issuing Fatwas was asked: In a number of
ahaadeeth it says “trim the moustache”. Is shaving different from
trimming? Some people trim the first part of the moustache that is
closest to the upper lip, and they leave the hair of the moustache, so
they trim nearly half of the moustache and leave the rest. Is this
what is meant? Or does trimming the moustache mean shaving off all of
it? Please advise me of the manner in which the moustache should be
trimmed.
They replied:
The saheeh ahaadeeth from the Messenger of Allaah (peace and blessings
of Allaah be upon him) indicate that it is prescribed to trim the
moustache. For example, the Prophet (peace and blessings of Allaah be
upon him) said: “Trim the moustache and let the beard grow; be
different from the mushrikeen.” (Agreed upon). And he (peace and
blessings of Allaah be upon him) said: “Trim the moustache and let the
beard grow; be different from the Magians,” and in some versions it
says: “Trim the moustache.” Trimming means cutting it very short. The
one who cuts his moustache very short so that the upper lip is visible
or trims it is not to blame, because the ahaadeeth mention two things,
but it is not permissible to leave the edges of the moustache, rather
the whole moustache should be trimmed or cut, in accordance with the
Sunnah
Source: http://islamqa.info/en/ref/103623