Question: Do I need to place a mezuza on the entrance to a laundry room or walk in wardrobe?
Answer: The Shulchan Aruch (YD 286:2) writes that utility and storage rooms require a mezuza. The Gemara (Sukka 3a) writes that we are not required to attach a mezuza to a house which is smaller than four amos by four amos. This ranges from 3.7m2 (R’ Chaim Naeh) to 5.9m2 (Chazon Ish).
While the Rosh (Hilchos Mezuza 16) writes that both the width and length of the room needs to be at least 4 amos, Rambam (Mezuza 6:2) and Shulchan Aruch (YD 286:13) writes that it depends only on the size of the area. Thus, the Shach (YD 286:23) and Aruch Hashulchan (YD 286:21) hold that one should affix a mezuza without reciting a beracha.
The Pischei Teshuva (YD 286:11) quotes Teshuvos Chamudei Daniel who holds that a room that if it is normal for a room to be less than 4 amos by 4 amos then it still requires a mezuza (See Minchas Yitzchak 4:92; Yechave Daas 4:51).
R’ Shmuel Wosner (Shevet Halevi 2:152) writes that if the laundry room contains soiled clothes and is less than 4 amos by 4 amos it doesn’t require a mezuza.R' Yitzchak Yaakov Weiss (Minchas Yitzchak 3:103) writes that a small closet just used for storing things or hanging clothes does not require a mezuza.