Alice Cooper, Edmonton 1975
A bandaged Alice continues to perform, Edmonton 1975.

This happened in Vancouver on the '75 'Welcome To My Nightmare' tour.

Alice slipped and fell into the photo pit in front of the stage, tried to do a few more songs, passed out, went to hospital. Photos exist of Alice trying to continue the show with his head wrapped in a bandage

The press reported at the time:

"It was such a silly thing. I was using a toy box as a prop, and it fell over and knocked me off the stage. I cracked my ribs and hit my head on the cement floor. I put my hand on my head and it felt like a baseball. But we came back on in that old 'the show must go on' bit. You get so much adrenaline while you're on stage you don't feel it, so when they asked me to come back on stage and do a couple of numbers so the kids wouldn't tear up the place or something I did it. I didn't really feel that bad for a while."
With a bandage on his head, Cooper stayed on stage for a couple more songs before exciting for a local hospital emergency room. The fall came during 'Welcome To My Nightmare', the first song of the evening's performance.

Rolling Stone - 13th July 1975

The status of Alice Cooper's tour was thrown into doubt after he fell off the stage during his June 23rd ('75) Vancouver show, breaking six ribs and suffering a concussion. The accident occurred after the opening number, 'Welcome To My Nightmare', as Alice chased the nightmares into a ten-foot-tall toy box. The box tipped over, flipping Alice on his head into the security barriers.

After being treated in the dressing room, Cooper returned to the stage wrapped in bandages. He was able to perform several numbers before ending the abbreviated show to cheers from the 17,000 in attendance. He was then driven to the local hospital, where he received 15 stitches to his head.

Alice appeared against his doctor's advice at his next date, in Edmonton, three days later, although warning the crowd he wasn't fit enough to put on an entire show. 35 minutes into the performance he collapsed after experiencing breathing trouble. Ticket refunds were offered, although no one was reported to have asked for one.

The next day, manager Shep Gordon sounded a pessimistic note on the status of AC's next show, in Minneapolis June 28th: "Everybody around him says he looks horrible."

But on the day of the performance, a publicity aide to Cooper said he was feeling "pretty spirited" and that the show would go on, adding "he's just going to be really careful."

The following next show in Edmonton three days later Alice managed to play around 35 minutes before having to give up. However 2 days later he performed the full show in in Minneapolis.

Alice Cooper, Edmonton 1975
Alice in Edmonton, unable to continue a few days after the fall, 1975.

In August 2008 he did it again!! Well not quite. At a show in Redmond, Oregon Alice took a fall and broke his ribs again, although he didn't actually fall off stage.

The current "Psycho-Drama" tour — approximately 100 shows from July 5 to December 4 — is still as physical as ever. In Redmond, Oregon last week, fans watched fascinated as Alice took a violent fall. Few noticed just how crushing the thud was. Most figured it was part of the show. Alice, hurting, continued with the performance and with a few performances after that, negating any suggestions to get himself checked out. Finally, giving in to those whose job it is to keep him healthy, he learned he had broken a rib and suffered ligament damage. Doctors advised him it would take three weeks of inactivity and rest to fully recover.
Fat chance. Cooper continues on tour, unrestrained.
(Press Release, August 2008)

That was the official line, however when talking to the Las Vegas Post Alice told a slightly different, if no less painful story:

"I just got back from the emergency ward. I have two broken ribs. During one segment in the show, the 'Welcome to My Nightmare' segment in about the middle of the show, they change everything — all the lights go down, the zombies come out. During the *rehearsal* I got knocked into a staircase and broke two ribs, so I can't swing a [golf] club for another two weeks. It makes the hanging scene a little harder. When you get hung you have this jolt. The floor drops out and the device that keeps you from really hanging gives you a darn good jolt. Yeah, my rib lets me know that’s not my favourite part of the show."