The Welsh international assumed the role after his fellow midfielder finally broke down with an ongoing hip problem which has plagued his season.
Ledley, while delighted to accept the accolade, is looking forward to handing the armband back.
"Scott is the man," he said. "It is nice to be given the captaincy while he is out and it's an honour to take it, but I'm looking forward to handing it back as well. Basically, I'm looking after it for him – but it will be back to him as soon as he is fit again.
"He has shown that he has all the attributes of a top captain and there is no doubt that we have missed him.
"The sooner he is back the better, but for his sake he needs to get the treatment and the rest that he needs to come back and be at his best."
Ledley had a similar issue to Brown, but an injection has saved him from requiring further treatment.
He was named in Chris Coleman's Welsh squad yesterday for the forthcoming World Cup qualifier which will mark Gordon Strachan's first competitive clash as Scotland boss.
While Ledley has lamented the absence of Brown in the Hoops squad, he is quietly pleased that he won't be lining up against his team-mate at Hampden next week.
"There was a wee bit of banter leading up to the last game, but there hasn't been too much in the build-up to this one," he said.
"For Wales, it is to our benefit that Scott is out because there is no doubt that he brings so much to the Scotland midfield."
Ledley, meanwhile, is looking for a recovery from Celtic after defeat to Ross County last weekend as Neil Lennon's side close in on a second successive SPL title.
"We want to finish with the best tally that we can and hopefully go unbeaten between now and the end of the season," he said.