Murphy limped off during the 3-2 home defeat to Hull on Saturday and must now have exploratory knee surgery to try and discover the extent of the cartilage problem.
The minimum time he will be out for is six weeks but the worst-case scenario would see him on the sidelines until April.
"We won't know exactly what the situation is until Murphy has had the operation on Thursday evening," Birmingham manager Lee Clark told the club's official website.
"He's damaged his cartilage and it could be anything from six weeks to five months. Obviously we are hoping that it is not very serious because we all know he's a very important player to us. We will have to wait and see."
Birmingham have therefore moved to retain the services of Robinson, with the former West Brom and Bolton defender due to stay at St Andrew's for a further two months, where he will look to add to the eight appearances he has already made for the club.
Robinson is predominantly used as a left-back but has also filled in at right-back and centre-back.
"I think we have all seen how well Robbo has done, and in three different positions," added Clark.
"Since coming in he has played an important part for us and been very consistent in his performances.
"We were always looking to extend the contract for a longer term and obviously with Murph now having surgery, he's going to remain a vital player for us."