United lost George in the first 10 minutes of their 1-1 draw with Leicester City on Sunday, with the defender immediately waving for help when she fell.
"It's an ACL. There are different levels of ACLs. She goes in today for an operation," Skinner told MUTV.
"I would always put 12 months (out of action) on this sort of injury. She could come back sooner, but I would rather work back. That's the sensible way to prepare, working backwards.
"We will support her and give her the best treatment and we will make sure that she comes back from that stronger and even better than she was before."
George joins United teammate Emma Watson (17) on the sidelines after the midfielder also suffered a similar injury while on international duty with Scotland last month.
The number of ACL injuries was a main storyline in the build-up to the Women's World Cup, with numerous high profile players missing the global showpiece, including England captain Leah Williamson (26).
United next face Paris St Germain in a Champions League tie on Wednesday, before travelling to take on Everton in the WSL.
