"We expect him to make a full recovery," Spielman said, via The Star Tribune, "and definitely be ready by the regular season."
Signed to a five-year, $31.5 million contract in March, Joseph is a key run-stuffer in head coach Mike Zimmer's defense.
He has released a statement regarding Saturday night's incident.
"I appreciate everyone's thoughts and concerns over the past 24 hours," Joseph stated. "I am extremely thankful that this was a minor injury for me. As the team has communicated, this was an unfortunate situation where I, along with several others, was an innocent bystander to a senseless act. My thoughts are with all of the victims at this time. I am looking forward to getting back onto the field with my teammates in the near future."