She and Lord Sugar - who chooses the victor in the BBC1 series - have gone into partnership to set up a range of cosmetic surgery clinics, after he invested £250,000 in her business.
Totton, who is the ex-girlfriend of Celtic's goalkeeper Fraser Forster, launched her Dr Leah outlet in Moorgate, central London, accompanied by Lord Sugar's aide from the programme, Karren Brady, and told of her stance on withholding treatment from young people.
She said: "Whilst we acknowledge that Botulinum toxin is used to treat medical conditions in all age groups, we cannot accept that its use as anti-ageing treatment in teenagers is in any way justifiable.
"It is our position that this is extremely poor practice and raises important ethical concerns. Dr Leah Clinics will not be treating teenagers with Botulinum toxin for the prevention of lines and wrinkles."
Medically-trained Totton's pledge came after some investigations found that some clinics have been willing to offer the treatment to people as young as 16.
Her clinic will offer a range of procedures, including facials, skin peels and botox jabs.
Lord Sugar applauded her stance, saying: "I chose Leah as my business partner not only because she has great entrepreneurial spirit, but she is also a fully trained doctor who is passionate about bringing regulation and excellence to the aesthetics industry.
"By stating that she will refuse to treat teenagers in her clinic is a bold but sensible move and I look forward to seeing her continue to pioneer safety and regulation in what is currently an unregulated marketplace."