The Super Kings on Saturday revealed Raina had left the United Arab Emirates to return to his homeland three weeks before the tournament gets under way.
"Suresh Raina has returned to India for personal reasons and will be unavailable for the 2020 IPL season. Chennai Super Kings offers complete support to Suresh and his family during this time." CSK chief executive KS Viswanathan said in a statement.
The announcement comes a fortnight after the 33-year-old retired from international cricket.
The loss of Raina is another blow for CSK in a week when at least 10 members of their camp reportedly tested positive for coronavirus.
One India player is said to among those who returned positive tests, with the majority being members of the support staff.
Fleming is without Suresh Raina and Harbhajan Singh, who opted out of the tournament that has been moved to the UAE amid the on-going effects of the coronavirus pandemic.
Ruturaj Gaikwad and Deepak Chahar also tested positive for COVID-19, along with several members of support staff, while a number of Fleming's first-choice personnel - the likes of Shane Watson, MS Dhoni and Ambati Rayudu - are short of competitive action due to the wider realities of 2020.
"It has been different, and that's been part of the challenge - understanding the unknown," Fleming said.
"We didn't get off to a great start, with some positive COVID-19 cases, but I think we dealt with it very well.
"We were calm around our approach, looked after the players and staff very well, and the rest of the players were calm in the hotel room. There was a bit of anxiety wanting to get out and train.
"It is what it is, and the players dealt with it very well. In hindsight, the amount of pre-season training that we've done up to now, and the extra few days in the room, was probably a blessing."
Mumbai's reasons for trepidation are more historically based.
The last time the IPL was moved to the UAE in 2014, they lost each of their five games.
"We didn't have a great experience last time yes, but it's a different team now," skipper Rohit Sharma said.
"The thought process is different. Six years is a lot of time. Like I said, it's about understanding pitches and conditions, that is crucial so we are putting a lot of emphasis on that.
"Eventually the pitches will play a big part, so understanding and adapting quickly is important. But yes, the past won't play any part - it was just myself, Kieron Pollard and Jasprit Bumrah from that team.
"I think Bumrah played just one game. So the team is different, the staff is different [and] thought process is different. Looking forward to a great IPL."
