"Unfortunately Birmingham is too soon, but I'm working really hard to get back as soon as possible and - of course -keeping everything crossed for Wimbledon," the 29-year-old wrote on Twitter.
The injury comes as a blow for world number five Kvitova ahead of next month's Wimbledon, where she will bid for her third title following triumphs in 2011 and 2014.
The LTA confirmed American Madison Keys has also pulled out of the tournament due to an injury.
World number three Karolina Pliskova joins a draw which already features world number one Naomi Osaka and newly-crowned French Open champion Ashleigh Barty.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
