The Torah prohibits the wearing of a garment which contains shatnez. Shatnez is a garment which contains both wool and linen.
One is permitted to wear tzitzis even if it contains shatnez because a positive commandment overrides a negative commandment. Wearing tzitzis is a positive commandment (You shall make tzitzis) and the prohibition of wearing shatnez is a negative commandment (And shatnez you shall not wear).
The commentary known as the Ra’avid holds that the permissibility to wear tzizis containing Shatnez only applies to wearing them during the day. However, one may not wear tzitzis containing shatnez at night because at night there is no commandment to wear tzitzis. The Mitzvah to wear tzitzis is only during the day, so at night when there is no positive commandment to override the negative prohibition of wearing shatnez, one can not wear tzitzis.