Are botox or hyaluronic acid injections not recommended for someone on antidepressants?

Unrelated. Injectable therapy should not have any physiologic effect on antidepressant medication. The two can be used simultaneously in a safe fashion.
No. The is no contraindication to using either of these products in a patient on antidepressants as long as the patient is competent to make the decision to use them.
Botox & filler. Many office cosmetic treatments are generally safe for patients on medications. Botox and hyaluronic acid injections (restylane, juvederm) have no known interaction with antidepressant medication. Speak with your dermatologist or plastic surgeon regarding any concerns you have.
Botox and Antidepres. There is no problem combining Botox , hyaluronic acid injections with antidepressants. Go ahead and treat those wrinkles.