If you have already submitted your tax return you would not need to do anything. If your tax return is rejected you can correct the middle initial and then re-submit. If accepted, you will be fine and you can correct it on next year's tax return.The IRS only verifies that the beginning letters of the last name and Date of Birth matches what the Social Security Administration has on file for you.
"TurboTaxDana , MBATurboTax Tax Support Agent"