All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The scholars have stated that the Hadeeth of Ibn Mas‘ood that reads, "The Prophet, sallallaahu ‘alayhi wa sallam, cursed the women who practice tattooing and those who get themselves tattooed, those who remove their facial hair, and those who create a space between their teeth to look beautiful…" is indicative of the prohibition of changing the creation of Allaah, the Exalted, either by addition or omission for beautification purposes. This applies to women who make gaps in their teeth or slim the teeth for beautification purposes. There is no doubt that closing the gaps between teeth is forbidden as well if it is done for beautification purposes.
However, if a woman closes the gaps in her teeth for medicinal purposes, then it is permissible. Ibn Hajar said in his explanation of "creating gaps in the teeth for beautification purposes": "It is disliked to create spaces between the teeth in order to look beautiful; however, if the woman needs it for curative purposes, for example, then it is permissible." [Fat-h Al-Bari]
Allaah Knows best.