The Torah says, "You will see [the tzitzit] and thus remember all the commandments of G‑d." From this verse it was deduced that this mitzvah is relegated to the daytime--the natural time for seeing. Nighttime clothing is exempt from tzitzit.
One is not precluded from attaching tzitzit to a night garment, but the mitzvah can be performed only with daytime garb, and the blessing for tzitzit may only be recited during daylight hours.
A tallit gadol (prayer shawl) may not be worn by night.
Definition of Terms
The definition of "daytime" and "nighttime" clothing is the subject of dispute between the medieval halachic scholars. One opinion is that no matter the type of garment, when worn during daytime hours it is obligated in tzitzit and when worn at night it is exempt. Others maintain that only a garment designated for nighttime use, such as pajamas, is exempt from tzitzit—even during daylight hours. Conversely, a garment which is normally worn during daytime is obligated in tzitzit even during the nighttime.
One may begin wearing a tallit and reciting the tallit or tzitzit blessings as soon as it would be possible to distinguish between the white and blue fringes of the tzitzit. Click here to find out this exact time for any location or date. The blessings may be recited, and a tallit worn, until sunset.
Despite all the above, many are careful to wear tzitzit even during the night, and even while sleeping.
There are several reasons for this practice: a) As mentioned above, according to certain opinions, one can fulfill the mitzvah of tzitzit during the night if wearing a designated day garment. b) If waking up after daylight, one will have fulfilled the mitzvah of tzitzit during the morning hours which have elapsed before his wakening. c) According to kabbalah, tzitzit afford a measure of protection to its wearer even after dark.
If one wears tzitzit while sleeping, it is preferable to have "night tzitzit." Otherwise, if one wears the same pair of tzitzit night and day, reciting the blessing on the tzitzit in the morning is problematic, for a new mitzvah is not being performed—it is merely a continuation of the mitzvah from the day beforehand. However, when putting on a different pair of tzitzit in the morning there is no problem with saying the blessing on the new pair—new mitzvah.