Blues have just two wins in 15 games since Gianfranco Zola was appointed as manager, replacing Gary Rowett in mid-December.
But Monk, who is banned from the touchline for his part in the melee at the end of Leeds’ loss to the Terriers last month, is taking nothing for granted.
“The Championship doesn’t allow you to relax for a second, not for a moment,” he said.
“Since they changed their manager it probably hasn’t gone as smoothly results-wise as they would’ve liked.
“That squad has been competing for play-off places over the last couple of seasons.
“They got a good result against Wolves, that will give them confidence.
“They have the quality within that squad to do much better than they have.
“They’ll be wanting to build on that game, so we’re expecting a tough game.
“That win will give them confidence, so we have to be ready.
“It would be a mistake not to show the respect that Birmingham need, just because they have had a difficult time.”
Monk’s own future was raised at the pre-match media conference, but he insists he is concentrating on accumulating points.
He added: “I haven’t spoken to the club. I’m contracted until the summer and I’m sure there will come a point where we will discuss the future.
“There’s plenty of time left. That’s not important right now. The most important thing is we focus on the game on Friday.
“My focus is on right now. We haven’t achieved anything yet. We have to stay focused.”
Monk is banned from the touchline for one game after accepting a Football Association improper conduct charge for his clash with Huddersfield’s David Wagner, who was banned for two games.
“I don’t see it being a problem,” said Monk, who also served a one-game touchline ban in October.
“Our players know exactly what they need to deliver and how they need to deliver it on the pitch against Birmingham. We fully trust the players.”
Birmingham v Leeds team news
“Jacques has been training with us three or four times already now,” Zola said.
“He is doing very well. It is just about getting him match fit.
“Jonathan Grounds and Lukas Jutkiewicz are now back training with us. So that’s good news, too.”
Centre-half Michael Morrison remains a couple of weeks away following his groin surgery, but striker Clayton Donaldson (heel) is nearing a return to full training.
Defender Paul Robinson is available after his red card received against Wolves was rescinded on appeal.