Zverev lost a five-set marathon to France's Arthur Rinderknech and later told reporters he felt "empty" and was considering therapy.
"Alexander Zverev has unfortunately withdrawn from the EFG Swiss Open Gstaad 2025 for personal reasons," organisers said.
They added that defending champion Matteo Berrettini would also miss the event due to injury. The Italian also suffered a surprise first-round exit at the recent grasscourt Grand Slam.
The Swiss Open begins on Monday.