EXCLUSIVE

1:18 PM PT -- Sinead was found at a hotel near Wilmette and taken to a nearby hospital ... according to Chicago local news.

12:15 PM PT -- Cops say they found Sinead and she is safe. She is no longer listed as missing and in danger.

Sinead O'Connor has gone missing, and police have reason to believe she's at risk of suicide.

The singer went out on a bicycle ride Sunday around 1 PM in the Chicago suburb of Wilmette, and has not been seen since. Someone called cops to report she hadn't returned from the bike ride ... and officers are now searching for her.

According to an alert sent out by cops ... O'Connor is being classified as "missing suicidal." She was last seen on a Raleigh motorized bicycle with a pink basket. She's not exactly in typical cycling gear -- black parka, black leather pants and a sweatshirt with "Ireland" on the back.