Malinga, who announced that he will retire after the T20 World Cup in 2020, was bought at the auction for INR 2 crore (£220,000).
But he has ruled himself out of at least Mumbai’s first six games of the Indian Premier League.
It comes with Malinga keen to be part of Sri Lanka’s squad at this summer’s World Cup, being held in England.
Sri Lanka’s selectors have told players that they must play in the forthcoming Super Provincial One Day domestic tournament if they are to be considered for selection at the World Cup.
That tournament runs from April 4 to April 11, with squads expected to be training for a few days before the action gets underway.
Malinga is currently in South Africa with Sri Lanka facing the Proteas in the final T20 today.
And the 35-year-old has revealed he wanted to miss the one-day domestic tournament to play IPL.
“I had asked the board for the No-Objection Certificate for me to play in the IPL,” Malinga told ESPNcricinfo.
“They had said that was fine, but that all players who want to go to the World Cup would need to stay back for the provincial tournament
“So I told them I’d play in the provincial tournament, and I asked the board to inform Mumbai Indians and IPL, since it was their decision.
“I’m ok with losing those earnings from IPL. I’m doing it for the country.”
And Malinga admits it may be best for Mumbai Indians to replace him permanently for the season.
He added: “Once I become available for Mumbai Indians, I would have missed seven or eight games.
“So there’s probably no point in them waiting around for me. Better for them to find someone else to replace me with.”
Mumbai Indians face Delhi Capitals today before a clash with Royal Challengers Bangalore on Thursday.
They then face Kings XI Punjab next Saturday.