Del Potro was eliminated by Andy Murray in the third round of the French Open earlier this month - a tournament which saw him struggle with a groin injury throughout.
The 28-year-old Argentine is still suffering from the problem and will now take the opportunity to rest in an effort to be fit in time for Wimbledon.
British number three Evans also faces a race to be fit in time for SW19 after suffering a calf injury during a tournament in Surbiton last week.
The 27-year-old was forced to retire during a quarter-final match with Dustin Brown and also pulled out of this week's Aegon Open in Nottingham as a result of the injury.
Jamie Ward - a semi-finalist in 2011 - has been given a wildcard into the tournament as he continues his recovery from a knee injury, but he is currently ranked outside the top 1,000.