To find the appropriate translation, you should provide more context as there are various situations where “This is my teacher” can be used in English. Depending on them, the French translation might vary. Here are some examples:

Introducing your teacher to someone else:

• Voici mon professeur.
• Je vous présente mon professeur.

Showing a photo of your teacher:

• Voici mon professeur.
• C’est mon professeur.
• Lui/elle, c’est mon professeur.

Showing your teacher among other people :

• Celui-ci / celui-là / celle-ci / celle-là, c’est mon professeur.

Notes:

• Professeur is written French and rarely used in spoken French unless formal speak, otherwise prof is used. Prof is both masculine and feminine while professeur generally stays masculine regardless of the teacher’s gender.

• A primary school teacher will translate to maitre or maitresse.

• For higher levels, there is more than one teacher so usually what is taught is specified (e.g. lui, c’est mon prof de math, elle, c’est ma prof d’espagnol)