Newly promoted Cottagers to visit Portman Road
Blues will face Premier League side Fulham at home in the second round of the Carabao Cup.
The winner of the tie will then host the winner of Rochdale or Sheffield Wednesday in the third round.
A Freddie Sears brace and a Luke Chambers header saw Blues progress in the first round with a 3-0 victory over Bristol Rovers.
Fulham, meanwhile, were given a bye in the first round due to their Premier League status.
Second round ties are set to take place on the midweek of 15/16 September, with the third round scheduled for a week later on 22/23 September.
Blues will announce a confirmed date and time for the Fulham tie in due course.
The second round draw for the South section in full is below.