Williams is trying to win an eighth title at the All England Club and a 24th Grand Slam trophy overall — an achievement that would equal Margaret Court's all-time record.
The 33-year-old Strycova had been pondering retirement this year but now is the oldest first-time major semifinalist in the professional era. It took her 53 major tournaments to get this deep.
In the first semifinal, also on Centre Court, former No. 1 Simona Halep will face Elina Svitolina.
Like Strycova, Svitolina has never before been to the final four at a major tournament.
Halep won the French Open last year and is trying to reach her fifth major final.