A fluid dispenser assembly comprising: a fluid dispenser (1) defining a substantially flat body (10) provided with a dispensing orifice (12) and with a removable closure member (15) masking the dispensing orifice; and packaging (2) encasing the body (10) of the dispenser while leaving the removable closure member (15) accessible so that it can be removed from the body; said dispenser assembly being characterized in that said packaging (2) comprises: a casing portion (3) containing the body (10) of the dispenser; and a substantially plane portion (4) connected to the casing portion (3) by zones of least resistance (43), so that the casing portion (3) can be separated from the plane portion (4).