Wimbledon increased its security in coordination with London police and other agencies for this year's tournament, in part as a result of protests at other major sports venues in Britain this year.
The rain had already created a major backlog of matches after the first two days, and only eight matches were completed on Tuesday. Several matches scheduled for the outside courts on Wednesday were pushed back to Thursday.
Only Centre Court and No. 1 Court at the All England Club have roofs.
On Centre Court on Wednesday, top-seeded woman Iga Swiatek eased into the third round with a 6-2, 6-0 win over Sara Sorribes Tormo, hitting 27 winners compared to just three for her opponent.
Defending men's champion Novak Djokovic was up next, facing Jordan Thompson of Australia in the second round.
On No. 1 Court, third-seeded Daniil Medvedev beat British 20-year-old Arthur Fery 7-5, 6-4, 6-3.
American duo Taylor Fritz and Frances Tiafoe both reached the second round, but in contrasting fashion. The ninth-seeded Fritz came from a set down to beat Yannick Hanfmann of Germany 6-4, 2-6, 4-6, 7-5, 6-3 on No.