Publicist Linda Dozoretz says the 81-year-old singer is recovering at a hospital after the New Year's Eve surgery.
Dozoretz says Bacharach's prognosis is excellent, but he will need to postpone scheduled concerts through mid-March.
Performances in Australia, New Zealand and Palm Beach, Fla., will be rescheduled for later in this year or early next year.
Bacharach most recently performed on Dec. 19 in Italy.