Fitting false teeth to replace teeth that have been taken out because they were unhealthy or damaged is something permissible and there is nothing wrong with doing it, and we do not know of any scholar who disallows it. It makes no difference whether the teeth are fixed in place in the mouth or not. The patient should do what is best for him in consultation with a specialist in that field.
Changing the creation of Allah means not accepting the creation of Allah with regard to the length or shape of the teeth or the gaps between them. Hence the one who changes the creation of Allah in general is cursed, and the one who changes it with regard to his teeth in particular is cursed.
Allah says (interpretation of the meaning):
“They (all those who worship others than Allah) invoke nothing but female deities besides Him (Allah), and they invoke nothing but Shaytaan (Satan), a persistent rebel!
118. Allah cursed him. And he [Shaytaan (Satan)] said: ‘I will take an appointed portion of your slaves.
119. ‘Verily, I will mislead them, and surely, I will arouse in them false desires; and certainly, I will order them to slit the ears of cattle, and indeed I will order them to change the nature created by Allah.’ And whoever takes Shaytaan (Satan) as a Wali (protector or helper) instead of Allah, has surely, suffered a manifest loss”
It was narrated from ‘Abd-Allah ibn Mas’ood (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “May Allah curse the one who does tattoos and the one who has a tattoo done, the one who plucks eyebrows and the one who has her eyebrows plucked, and those who file teeth for the purpose of beautification, changing the creation of Allah.” Narrated by Muslim (2125).
Al-Nawawi (may Allah have mercy on him) said:
The one who does tattoos is the one who uses a needle and the like on the back of the hand, wrist, temple or other place on a woman’s body where blood flows, then fills that place with kohl etc and it turns blue.
“The one who plucks eyebrows” is one who removes hair from the face.
“Those who file teeth” refers to women who file the teeth to create a gap between the front teeth and second incisors. This was done by elderly women and those of similar age to make them look younger and to make the teeth look more beautiful, because it is younger girls who have these nice gaps between their teeth. When a woman grows older her teeth become bigger, so they used to file them to make them look nicer and to make people think they were younger. This action is haraam for the one who does it and the one to whom it is done, because of these ahaadeeth, and because it is changing the creation of Allah, and because it is cheating and deceiving people.
“Those who file teeth for the purpose of beautification” – this indicates that what is haraam is that which is done for the purpose of beautification. But if it is needed for medical reasons or to correct a fault in the tooth and so on, then there is nothing wrong with it.
Sharh Muslim (14/106, 107).
The words of al-Nawawi point to the difference between treating the teeth in order to remove a fault in them and not being pleased with the creation of Allah and tinkering with it for the purpose of beautification. The former is permissible and the latter is haraam.
There is evidence in the Sunnah which shows that it is permissible to wear false teeth if the teeth have fallen out due to old age or sickness, and it is permissible for them to be made of gold if nothing else can be used.
It was narrated from ‘Arfajah ibn As’ad that his nose was cut off at the battle of Kilaab during the Jaahiliyyah, and he wore a nose of silver, but it caused a foul stench, so the Prophet (peace and blessings of Allah be upon him) told him to wear a nose made of gold.
Narrated by al-Tirmidhi (1770), Abu Dawood (4232) and al-Nasaa’i (5161). Classed as hasan by Shaykh al-Albaani in Irwa’ al-Ghaleel (824).
The scholars of the Standing Committee said:
But in cases of necessity it is permissible to use gold for teeth, noses and the like, if nothing else can be used instead. End quote.
Fataawa Islamiyyah (4/248).
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said:
We should note that it is not permissible to have a gold tooth except when there is a need for that. It is not permissible for anyone to have a gold tooth put in for the purpose of adornment, except women for whom is it customary to have gold teeth, in which case there is nothing wrong with it. But for men it is not permissible at all except in cases of necessity.
(Source - Islam Q&A)