I'm aware of phishing and scam risks, of course, and I would not touch this without contacting Amazon directly first(I have a dedicated e-mail address.).
However, experience tells me that the members of this forum are often aware of these things long before official channels!
Further study of the email (I was in a rush to get out this morning) reveals that Amazon have found my email/password on another site (what were they doing there?) and immediately changed the password , and sure enough I cannot log in.
They advise me to go to "Mt Account" on the Amazon website and use the "Lost Password" option. (There are no links anywhere in the email.)
Very suspicious! I shall contact them during business hours tomorrow.
This happened to me a few months ago. Like you, Amazon had changed my password and I could not log in to my account. Followed their advice and reset to new password, obviously without following any links. Had no trouble since.
It occurred to me that maybe Amazon do this periodically as a matter of course if you have had an account for a long period of time. Either that or they have very strong fraud detection processes on board. In my case possibly they discovered that my email address had been compromised and found its way onto spammers lists.