No, they do not. You were wise to be suspicious of the email. See Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams - Apple Support. You can forward the email to , and then delete it.

How does Apple notify you of suspicious activity?

For the record, Apple will never call you to notify you of suspicious activity. In fact, Apple won't call you for any reason—unless you request a call first. Phone scams like these are also known as vishing. ... Then you'll see a pop-up message on your phone saying that it will remain locked until you pay a ransom.

Does Apple email you if your account has been hacked?

Signs your Apple ID has been compromised

You receive a confirmation email from Apple that your Apple ID password was changed or your account information was updated, but you don't remember making any changes. ... Your password no longer works, or it might have been changed or locked.