Beale left the stage during the second half of Wednesday night's performance, announcing he thought he had broken his finger.
Minutes later, his understudy Paul Dodds replaced him.
A spokeswoman for the theater told the BBC the transition between actors was "smooth."
"I didn't have time to get nervous," Dodds told the British broadcaster after the show. "It was about an eight-minute turnaround from Simon deciding he couldn't continue to me going on stage to replace him. I think I very quickly became some kind of pragmatist!"
The BBC said Beale went to St. Thomas' Hospital where he was treated for his injury.
"He had his fingers splinted at the hospital. It was his right hand so he has had to slightly amend his performance," the theater spokeswoman said.
Beale returned to the stage Thursday night.