The outdoor tournament is considered a key warm-up for the Wimbledon Championships, which start a week later.
Players will include 2025 Australian Open winner Madison Keys and home favourite Sonay Kartal, who is from Sussex.
Keys, who won the title in 2014 and 2023, is returning to the south coast in a bid to complete a hat-trick of titles at Eastbourne.
An LTA spokesperson said: “Devonshire Park is owned and operated by Eastbourne Borough Council and we are being kept updated about the incident and security on site.
“Ground staff are already working hard to repair the damage to the grass and there will be no impact on the Lexus Eastbourne Open.”