With boss Ronnie Moore woefully short in the forward line and any new deals unlikely at the moment, Marcus Marshall and Paul Warne will share the second strike birth with Alfie at the Impact Arena on Tuesday.
A disappointed Elliott told the clubs official site: "I was running in training and basically I just felt a sharp pain in my leg so I stopped.
"I spoke to both the Leeds and Rotherham physio's and they have said that it is only a small tear, so I should be okay again in a week. Hopefully I will be back for the friendly at Tamworth on Saturday.
"I think that the Gaffer was happy with me after the Leicester game, he told me beforehand to keep shooting which I did and I was happy with the display," he added.
"I enjoyed playing with Alfie and I thought that we worked well together. "I am enjoying the experience but I was a little gutted to miss the game against Sheffield United. My aim now is get back to full fitness and make sure that I am sharp for the first game of the season against Lincoln."
Kick off tomorrow night is 7.30pm, £7 on the gate.