If you are having your refund direct deposited, then no problem.
If you are paying your tax due, then no problem.
If you are receiving your refund by check, then it depends on whether or not the Post Office figures it out. Based on my experience, in most parts of the country the Post Office will figure it out once it gets to the right zip code.
However, you may want to update the IRS on the correct address after April 15th. See https://www.irs.gov/taxtopics/tc157 for the form to change your address.