Update 04/18/2019: The Nintendo of America Twitter account has announced that the issues with the eShop have been resolved, and access should now be available. It does warn that there may be intermittent errors, though.
Access to the Nintendo eShop has been resolved. However, some may still experience intermittent errors. We appreciate your continued patience.
— Nintendo of America (@NintendoAmerica) April 18, 2019
Original story: The Nintendo Switch eShop is down and experiencing issues following the release of Joker from Persona 5 and the Version 3.0 update for Super Smash Bros. Ultimate.
Source: IGN.com Update: Nintendo eShop Back Online After Release of Smash Bros. Joker