Raducanu was facing Switzerland’s Viktorija Golubic in a WTA 250 event in Nottingham when she felt as if she had “pulled something” on the side of her body.
But the US Open champion said she is eying up a return to the court later in the grass court swing.
“It was disappointing to go out this week with a side injury and unfortunately (I) will no longer be able to play in Birmingham,” Raducanu said in a statement released by the Lawn Tennis Association.
“I’m looking forward to being back on the match court soon though to enjoy the rest of the grass season.”
The 19-year-old Raducanu reached the fourth round of last year’s Wimbledon on her grand slam debut.
She then followed that up by winning the US Open in September but has struggled with form and fitness since her breakthrough last year and is currently without a coach.
On Tuesday, Raducanu said she had “no idea” whether she would be able to compete at Wimbledon, which begins on June 27.