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Play has been stopped 10 times in five days, leaving a backlog of matches that have to be played on the two-week tournament's traditional rest day.
There will be at least eight guaranteed singles' matches, plus any more which are not completed on Saturday.
Tickets must be purchased in advance online, with none available on the day.
Full Wimbledon forecast
Further details will be released at 13:00 BST on Saturday, added Wimbledon organisers.
Play will start on all courts, including Centre and Court One, at 11:30 BST.
It will be only the fourth time in Wimbledon's history - after 1991, 1997 and 2004 - there has been play on the middle Sunday.
Organisers were forced to close the roof on Centre Court on Friday, while Novak Djokovic - the defending men's champion - was two sets down against world number 28 Sam Querrey on Court One when play was stopped for the day about 20:15 BST.
"It was a pretty straightforward decision because we're here on Friday night and have still got second-round matches to be played," said former British number one Tim Henman, who is part of the Wimbledon organising committee.
"You have got to avoid sections of the draw getting too far apart and therefore have to hold those matches back.
"If we weren't to play on Sunday then we would have the scenario on the women's side where they would have to play third-round matches on Monday, fourth-round matches on Tuesday, quarter-finals on Wednesday and semi-finals on Thursday. And that's if we have good weather.
"From the tournament's point of view, our hand was forced. It is a good decision."
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Wimbledon will have play on the middle Sunday for the first time since 2004 after the opening week's schedule was disrupted by rain delays.