The 27-year-old's withdrawal comes after he was forced to retire from his match against Dustin Brown of Germany in the Surbiton Trophy on Saturday.
It is not yet known if Evans will be fit enough for Wimbledon, which starts on 3 July.
Meanwhile, fellow Briton Laura Robson went out in the first round at Nottingham, losing to Julia Boserup.
Robson, 23, received a wildcard for the grass-court event but was beaten 6-4 6-3 by the American world number 87 on Monday.
British number one Johanna Konta is the top seed in the women's draw and starts her campaign against compatriot Tara Moore on Tuesday, while Heather Watson faces American Alison Riske.
Elsewhere, Aljaz Bedene, the British number four, beat world number Denis Istomin of Uzbekistan 3-6 6-2 6-1 in the first round of the Ricoh Open in the Netherlands.
Following his withdrawal, Evans said: "The injury I picked up at Surbiton last week needs more rest before I can get back on court.
"This is my favourite time of the year so I'm getting treatment and will do everything to be ready for Queen's next week. Thanks for all the messages of support, it really means a lot."
Robson admitted she "did not do so well" on her return to the main tour, having played on the ITF circuit as she continues to rebuild her career after injury.
"I am disappointed with how it went because I had so many break-point opportunities, but I just couldn't make court on most of them," she said.
"It is a step up in level to what I have been playing and it might take me time to adjust to a different pace of ball, different tactics."
British number three and top seed Dan Evans has pulled out of the Nottingham Open with an injury.