The Argentinian striker, who had not played since September 2014 when he joined the Millers on a short-term deal in January, missed Saturday's 2-1 defeat at Bolton after picking up a calf injury in training.
He joins Leon Best and Stephen Kelly on the injured list, with all three men picking up injuries having had no football prior to their arrival at the club.
Best has had to undergo surgery on a groin problem which has kept him out since early December while Kelly has a calf problem with no return on the horizon.
Redfearn knows it is a dangerous game to pin his hopes on such signings, but says he has limited option.
“We are shopping at a
different market to everybody else,” he said. “The players we are bringing in
are good players, experienced players, and they are doing everything they can.
“But what happens when you’re picking up players who are out of contract is you have to get them up to speed quickly and it becomes difficult.
While Best and Kelly have had the Millers medical team working overtime, Becchio's problem is not thought to be serious.
“He has got a slight calf strain he picked up during the week,” Redfearn added. “He has done a lot in a short space of time after being out for a while. I think it is a superficial one.”
