Police were alerted after she went on a bike ride at 06:00 local time (11:00 GMT) on Sunday, and did not return.
O'Connor became a global star in 1990 with the worldwide hit Nothing Compares 2 U, a song written by Prince.
Local media report that she had been staying with friends in the Chicago suburb for the past several weeks.
She has recorded 10 solo albums but has also made headlines with controversial outbursts throughout her career.
In 1992, she ripped apart a photo of Pope John Paul II during a live television broadcast and has been a strong critic of the Catholic Church over its handling of the child abuse scandal.
And last week she was in the news again after alleging US comedian Arsenio Hall had supplied drugs to Prince, who died last month.
He strenuously denied the allegation and said he was suing the Dublin-born, mother-of four.