Yes. The spread at exercise is treated as wages for the purposes of withholding federal income tax, which is withheld at the minimum required withholding percentage for supplemental income. This flat rate is 22%, though the less common W-4 rate is permissible. (The withholding rate is 37% for aggregate supplemental income in excess of $1 million during a calendar year.)
Alert: As explained in another FAQ, the amount withheld at NQSO exercise may not cover the total amount of taxes you owe on the additional income, considering your marginal tax rate.
In addition, state tax withholding also applies (if your state has an income tax), along with federal FICA taxes (Social Security up to the yearly maximum and Medicare).
Your company will have a process for calculating and collecting this tax withholding and for sending it to the IRS. The money used for the taxes can be funds from the proceeds of any stock sale at exercise or cash that you give the company. To see how this withholding is reported on your Form W-2, see the annotated example in the Tax Center.