The stock was falling 6% on Wednesday to $137.94.
The Dublin-based pharmaceutical giant announced in a press release it would also stop selling its textured breast implants and tissue expanders.
France's National Agency for the Safety of Medicines & Health Products said in a statement late Tuesday it had not identified any immediate risk for women wearing the implants.
The New York Times reported the products, specifically the textured implant, have been linked to breast implant-associated anaplastic large-cell lymphoma. The lymphoma is not cancer, but a immune system disease that develops years after implant surgery.
The recall announced Wednesday comes after Allergan's CE mark, a European regulatory stamp of approval for medical devices, expired Sunday.
French health officials said it could not renew Allergan's CE mark because the company could not provide additional data requested on the textured implants before the expiration date.
The French regulator said the issues lie with Allergan's Microcell and Biocell products.
Allergan, the maker of Botox and Juvederm products, has been considering a sale of its women's health and infectious disease businesses, but the company said in October so far offers have been too low.