Former India captain Dhoni led the now-suspended Chennai franchise to Twenty20 league title victories in 2010 and 2011 but under his captaincy Pune finished second last in their maiden IPL season last year.
"I have the highest regard for MS Dhoni as a leader and a person. Dhoni will continue to be an important part of our team," Pune franchisee owner Sanjiv Goenka said in a statement.
"He is supportive of the decision keeping the franchisee's best interests in mind."
Dhoni, who quit test cricket in 2014, stepped down as India's limited-overs captain last month, having led the team to World Cup triumphs in both the 20-overs and 50-overs format.
Smith's Australia team mate and fast bowler Mitchell Starc has pulled out of this year's IPL which begins on April 5.
"After a long summer and with a big tour of India still ahead I think it is in my best interests, both physically and mentally, for me to have a break, spend time with my family and take the opportunity to work on getting back to full fitness," Starc said.
(Reporting by Amlan Chakraborty in New Delhi; editing by Ed Osmond)
