The 29-year-old Czech player was set to be the top seed at the WTA tournament played in the eastern Czech city of Ostrava on September 20-26.
"It is not really easy to excuse myself from a tournament played before an audience and at home," said Pliskova, who reached the Wimbledon finals and the US Open quarter-finals this year.
Her doctor said the injury had been apparent for a while.
"Problems with the wrist appeared even before the US Open, and they could not be treated adequately as she advanced in the tournament," Radek Kebrle said in a statement.
"Since the problem got worse, we have agreed on a three-week break from tournaments," he added.
Pliskova's withdrawal leaves Ukraine's world number four Elina Svitolina as the top ranked player in the tournament.