What do I file if I received a corrected 1099-NEC showing $0 income? I erroneously received a 1099-NEC for a non-taxable reimbursement.

If you filed a Schedule C and included the original amount from the 1099, then you must amend and enter zero for income. If you took expenses, then omit them. . If you did not include it, do nothing. 

It depends if you have already filed your return or not.  As leeloo posted, if you have already filed and included the amount on your tax return, you will need to amend your return.  See How to amend for more information.  If you did not include the amount on your return, regardless of whether or not you have filed it, you do not need to do anything.

If you have not filed your return, but included the amount you will need to delete the form.  

To delete a specific form in TurboTax Online you can follow these steps:

1. Within your return, click on Tax Tools in the black menu on the left side of the screen.
2. Click on Tools.
3. Click on Delete a Form. 
4. Scroll down to your form and click Delete.
5. Under Federal in the black menu bar click Wages & Income to get back into your tax returns.
6. Proceed entering/reviewing your return.

To do this in TurboTax Desktop you can follow these steps:

1. Within your return, click on the Forms icon in the upper right of the screen to switch to Forms mode.
2. Scroll down in the menu bar on the left and select your form.
3. Click the Delete Form button at the bottom left of the preview screen.
4. Confirm the deletion then click the Step-by-Step icon in the upper right of the screen.
5. Proceed entering/reviewing your return.

@sgv2