As electronic products, LEDs are regulated in the US by the FDA/CDRH, but are not subject to any performance standards or certification/reporting (self or otherwise).
The following apply to both US and primarily EU countries: 21CFR1040.10/.11 (regulation) for lasers and laser-based products in the US ANSI Z136 (standard) for laser product and workplace management IEC EN60825 (standard) for lasers and laser-based products in the EU IEC EN62471 (standard) for LEDs in the EU Although OSHA has a guidance document page,[…]
Yes and no. in the US, laser components must be registered, and product reports must be filed for laser-based products as per 21CFR1040.10/.11, but there are no regulations for LEDs or fiber optics. Overseas, the IEC, requires lasers to comply with IEC EN60825 and LEDs to comply with IEC EN62471.