No, but you will not be able to e-file your return.
According to the IRS:
A spouse who is Married Filing Separately is not required to provide the Social Security card for the other
spouse, although the return cannot be e-filed without the spouse’s Social Security number.
IRS link
Here is more information about filing with a nonresident spouse
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"
