He was later seen on set holding an ice pack on his arm and shared a video of himself being wheeled into urgent care before revealing an x-ray of his arm.
Joseph doesn't appear to have been seriously hurt, but it is unclear what the exact injury is.
'Power' features Jamie, 50, as a family man who has suffered a great loss, while Joseph stars as a cop who takes matters into his own hands and it centres on a drug epidemic that gives people superpowers.
Meanwhile, the 'Interstellar' actor - who has two sons, aged three and 15 months, with wife Tasha McCauley - previously admitted he finds the idea of celebrity "unhealthy" and he feels "bad" about his position in the public eye.
He previously said: "What I don't like [about acting] is: I guess since the heyday of Hollywood, there has been a merging of actors and royalty and celebrity.
"It's tough to complain, because it's a really privileged life I get to lead, [but] the whole celebrity thing is unhealthy and I feel bad perpetuating it."
