"We are obviously devastated, not only for the whole sport and squash fans everywhere, but for the players, current and future that have worked so hard for this," said PSA CEO Alex Gough.
"We can be very proud of the efforts of everyone and none more so than our world number one Ramy Ashour, who has put in so much time into the bid process," he said.
Wrestling, one of the rare sports which progressed from ancient to modern Olympics, won the poll in the first round of voting with 49 of the 95 votes cast. The joint bid of baseball/softball was second with 24 votes and squash received 22.
The result saw wrestling assured of appearing at both the 2020 - which is to be hosted by Tokyo - and the 2024 Summer Olympics.
"Our sport has much to offer the Games - let's hope that this is not the end of our Olympic journey.
