Moving Reimbursement W2 Error?

My new employer (W2) wrote me a check for moving expense reimbursement, separate from my payroll direct deposits.  This amount was not accounted for in my W2 for the year.  My understanding is that I still owe tax on the reimbursement (both federal and FICA since nothing was withheld).  Can I pay this through TurboTax somehow or do I need to request an amended W2 from my employer?