Height in a Shul:

According to all opinions, the Mechitza must be at least tall enough to reach the average shoulder height of a person, which is approximately 18 Tefachim.[1] If it is lower than this height, then it is completely invalid. Now, regarding if it must be even higher than average shoulder height, is disputed amongst the Poskim. Some Poskim[2] rule that it suffices for it to be of shoulder height and remains valid even if the men can see the uncovered hair of married women, although it is an act of piety for it to completely block also the faces of the women.[3] However, according to most Poskim[4], and so is the Rebbe’s opinion[5], it must be tall enough to completely block vision of the women, and hence it must be tall enough to block the men from seeing the heads and faces of the women. At minimum, it must be at least 6 feet tall.[6] This applies even if all the married women cover their hair, and certainly if they don’t. Some Poskim[7] rule it should be high enough to prevent the vision of men even when they are standing on the podium, such as on the Bima or steps of the Aron Kodesh. [Nonetheless, effort should be placed to have a Mechitza of the height of at least the lenient opinion, if the congregation refuses a Mechitza of the stringent opinion, and with time perhaps one can influence them to make it higher.[8] However, one should not accept the position of being a Rav in such a congregation[9], and perhaps should not Daven in such a congregation, as such a Mechitza is invalid according to the Rebbe and many Poskim.]

Height by an event:

Some Poskim[10] rule that only in a Shul is it required for the Mechitza to be the above height to completely block the sight of the other gender. However, by an event, such as a Sheva Brachos meal or Shiur, a simple divider of even ten Tefachim is valid.

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[1] Igros Moshe O.C. 1:39, 41-42 in negation of opinion that a Mechitza of ten Tefachim high and four Tefachim wide suffices [as is the law of a Mechitza by other Halachic matters]. This negated approach was seemingly the approach of Rav Y.B. Soloveichik, as brought in Mipinyanei Harav p. 46

[2] Igros Moshe O.C. 1:39, 41, 42; 2:40; 3:23-24

[3] The reason: As in their opinion, the main reason for the division is to prevent intermingling and not to block the view of the other gender. [Igros Moshe O.C. 1:39]

[4] See Divrei Yoel O.C. 10 in great length in negation of the opinion of the Igros Moshe ibid; Kaneh Bosem 2:9; Piskeiy Teshuvos ibid; All Poskim who rule the purpose of the Mechitza is to block the sight of the women: Maharam Shick O.C. 77; Zichron Yehuda O.C. 72; Divrei Yoel O.C. 1:10 in great length; Tzitz Eliezer 7:8 in name of 70 Rabbanim; Rebbe in Igros Kodesh 7:309; 14:228; 19:73; 23:156; Otzer Hamelech 3:146; Shevet Halevi 1:29; Beir Moshe 4:147; Mishneh Halachos 7:12

[5] Igros Kodesh 7:309; 14:228; 23:156; Otzer Hamelech 3:146

[6] Igros Kodesh 7:309; 23:156

[7] Kaneh Bosem 2:9

[8] See Igros Kodesh 14:228 for a similar response of the Rebbe, although to note that there it refers to a Mechitza that does reach head height of those women present, but not of all women, as explained in Pardes Chabad ibid

[9] See Igros Kodesh 23:156

[10] See Kiddushin 81a and Rashi ibid [brought in source #3]; Seridei Eish 1:77; Shevet Halevi 8:281; See Hiskashrus 588:11 that according to the Sefer Chassidim that the intermingling itself is forbidden, perhaps having separate seating suffices and having actual dividers is not necessary. However, according to the Sefer Minhagim Tirana, it is clear that a blocking divider is necessary