Defending champion Murray was scheduled to play Italy's Fabio Fognini in the last 16, while 2008 winner Rafael Nadal was set to face France's Gilles Simon.
British number one Konta, 25, saw her quarter-final against Germany's Angelique Kerber postponed.
The matches will all now be played on Thursday on Centre Court.
Andy Murray meets Fognini, ranked 40th in the world, about 17:00 BST, with Konta and Wimbledon finalist Kerber following them.
Fourteen-time Grand Slam winner Nadal, 30, starts on Centre Court at 15:00.
Konta and Jamie Murray will face Americans Bethanie Mattek-Sands and Jack Sock in the first round of the mixed doubles after 21:00.
