Speaking after the Liverpool game on Sunday, Solskjaer denied Rashford was already suffering from a back fracture before the Wolves match and reiterated that in his news conference on Tuesday.
"He's not had that injury before," he said. "He complained a little bit after Burnley [on December 28] - he felt it the first time, and we managed him as well as we could then.
"He had some days off for treatment, was taken off in games and suddenly this was a new injury. He didn't have any injuries before then."
Wright added: "Rashford has started every game and for him to play that much football, with the problems he is having with his back, you can't mess around with that and Solskjaer has to take some blame in still playing him."