Local media quoted Bangladesh Cricket Board officials saying Mushfiqur was tired of biosecurity measures brought in because of Covid-19.
The BCB chief cited Bangladesh's busy schedule and T20 World Cup as the reasons behind KKR all-rounder Shakib not getting a NOC from the board for IPL.
Bangladesh has announced the squad for the first two ODIs which will be played on Sunday and May 25 respectively.
Shakib had on Sunday claimed that the BCB has "misrepresented" his decision to play in the IPL at the expense of serving the national team in a Test series against Sri Lanka.
With the T20 World Cup slated for October, Shakib said there are many advantages of playing in the IPL this time.
The Bangladesh Cricket Board has allowed its players, including Mustafizur, to participate in the IPL despite the fact that the league is likely to clash with international assignments.
Abdur Razzak who featured for Bangladesh in 200 international games between 2004 and 2018, will have to call off his cricketing career to take up the job.
Apart from two small events last year and the current tour by the West Indies -- which were held in strict bio-bubbles -- all play has been suspended since March.
The ICC had charged Shakib with failing to report two approaches to engage in corrupt conduct during the tri-series and in an IPL match.