Darby is currently the first-choice right-back, ahead of club captain John Thompson, and has helped Notts keep five clean sheets in the 12 games he has played.
"He's been brilliant. He's a model professional and he has never let us down on any occasion. We're delighted to have him on board for the rest of the season," said Magpies assistant manager Alex Rae.
"He's still got another year to go with Liverpool. In terms of where we go, we'll have to look at it in the summer. How he does between now and then will be a factor."