Raducanu was taking on Switzerland’s Viktorija Golubic at a WTA 250 event in Nottingham when she felt like she had “shot something” into the side of her body.
But the US Open champion said she is considering a return to the court later in the grass 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 look forward to being back on the pitch soon to enjoy the rest of the season on grass.”
The 19-year-old Raducanu reached the fourth round of Wimbledon last year on her Grand Slam debut.
She 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” if she would be able to compete at Wimbledon, which begins June 27.