Yes, the 401(k) distribution to pay off a loan is taxable as for any other distribution from a 401(k). This is considered as a distribution as if the 401(k) paid the money to you and you paid off the loan.

If your wife is under age 59 1/2, she is also liable for an early withdrawal penalty of 10%.

This offset distribution, indicated with code M in box 7 of the Form 1099-R is eligible for rollover.  You have until the due date of your 2018 tax return, including extensions, to come up with the money to complete this rollover to another qualified retirement account like a traditional IRA.  Whatever amount you roll over will continue to have taxes deferred and avoid an early-distribution penalty.