If you're not already using 2FA for your account or any accounts that support it for that matter, now is a good time to make that happen as this servers a good reminder that a normal name and password combination is just no longer enough. You can easily set up 2FA in your account and can find the instructions in there on how to do so. Below is the statement from Nintendo:
We would like to provide an update on the recent incidents of unauthorized access to some Nintendo Accounts. While we continue to investigate, we would like to reassure users that there is currently no evidence pointing towards a breach of Nintendo's databases, servers or services. As one action in our ongoing investigation, we are discontinuing the ability to use a Nintendo Network ID to sign in to a Nintendo Account. All other options to sign-in to a Nintendo Account remain available.
As a further precaution, we will soon contact users about resetting passwords for Nintendo Network IDs and Nintendo Accounts that we have reason to believe were accessed without authorization.
During the investigation, in order to deter further attempts of unauthorized sign-ins, we will not reveal more information about the methods employed to gain unauthorized access. We apologize for the inconvenience and concerns caused to our customers, and we will continue working hard to safeguard the security of our users' data.