Required Mandatory Distribution

1.  Unfortunately, there is no way to avoid a potential increase in Medicare premiums caused by the Required Minimum Distribution (RMD).  Medicare premiums are not fixed for everyone, and vary based on your income.  If you have a higher income, due to your RMD or another reason, you’ll pay an additional premium amount.  Medicare premiums are calculated using your Modified Adjusted Gross Income amount from your most recent tax return.  Your Modified Adjusted Gross Income is your Adjusted Gross Income plus any tax-exempt interest income.  This link to the Social Security Administration website describes how adjustments to your Medicare premiums are made and includes a chart to determine the amount of the Medicare premiums.
2. Once you begin receiving RMDs, your “before tax” contributions to your 401(k), which were tax-deductible when you made them, will be treated as ordinary income for the year in which you receive the RMD.

I hope this is helpful.

You could avoid the RMD increasing your AGI by making a Qualified Charitable Distribution to satisfy your RMD.  However, QCDs are only permitted to be amde from IRAs, not from qualified retirement plans like a 401(k), so you would have to satisfy the RMD for the 401(k) before rolling the 401(k) over to a traditional IRA so that QCDs could be used to satisfy IRA RMDs for future years.