He is the second big casualty for Pune Supergiants after former England batsman Kevin Pietersen was ruled out due to calf muscle injury.
South African right hander Du Plessis took to twitter to confirm the development.
"And so my Ipl tournament unfortunately comes to and end. Broken finger and out for 6 weeks. Thanx India and @RPSupergiants it's been fun," he tweeted.
Du Plessis is Supergiants' second-highest run-scorer with 206 runs at an average of 34.33 in six matches. He scored back-to-back 50's against Gujarat Lions and Kings XI Punjab, both of which came in losing causes.
If Du Plessis is out of action for six weeks, he might also miss South Africa's tri-nation ODI series with West Indies and Australia.