Finch had been ruled out after suffering a hamstring injury during Mumbai Indians' match against Rajasthan Royals on April 14, while Hazlewood had opted out of the tournament keeping in mind Australia's tight international schedule.
While Munro is yet to play in the IPL, Hilfenhaus figured in 17 games for Chennai Super Kings, in 2012 and 2014, and took 22 wickets at an economy-rate of 7.72.
Fleming wants improvement from Ashwin, Jadeja
Stephen Fleming, the Chennai Super Kings coach, wants his main spinners R Ashwin and Ravindra Jadeja to improve their performance so far this season.
Super Kings have relied heavily on the duo over the years, but this time, they have managed four wickets between them in five matches. While Ashwin has conceded 8.16 runs an over, Jadeja's economy-rate is as high as 10.15.
"The spinning aspect of our game hasn't been as effective as it has in the previous years so far and it is one area where in this game we would like to get a bit more penetration," Fleming told the IPL website ahead of Super Kings' home game against Kings XI Punjab.
"But in saying that, we have won games despite our spinners not clicking. That is a good thing because in the past we have been called a team that relies too much on the spinners. If we can get the spin component going well at home, there will be an improvement.
"In our home games Ashwin has been our lead bowler. It is not that he is in bad form. Jadeja is someone we would like more from and we are working hard at it."
Both seamers have taken eight wickets each so far from five games. While Anureet has also been used at the death and has gone for 8.75 runs an over, Sandeep has struck consistently at the start and conceded just 5.55.
"Sandeep is showing great capacity of taking wickets upfront, which is very important," Bailey said. "A lot of teams look for a bowler who can break up the top order.
"Anureet has shown how versatile he is to be able to bowl at any stage of the game. He has taken well to the death-bowling role, which is a very difficult one. Our depth is pretty good. We have Shardul Thakur, who had an outstanding Ranji Trophy. But we haven't been able to get him in yet."