There is no "Married" filing status; there are "Married Filing Jointly" and "Married Filing Separately". As you are married as of the end of 2016, you may only file 2016 taxes as Married Filing Jointly or Married Filing Separately (or in certain situations if you have a dependent, you might be able to choose Head of Household), and cannot file as Single.
You are a resident alien for 2016, as you pass the green card test. I will assume that your wife hasn't been to the US much, so she is a nonresident alien for 2016, because she does not pass the green card test or the substantial presence test. In this case, there are basically two ways the two of you can do it:
- File as Married Filing Separately. This basically means you file as Married Filing Separately and she almost certainly does not have to file as nonresident aliens are only taxed on income connected to the US, and I'm assuming that she doesn't have any. Note that the tax calculated for Married Filing Separately is almost always worse than for Married Filing Jointly, especially if the two people's incomes are very different.
- File as Married Filing Jointly. Since one of you is a resident alien and the other is a nonresident alien, this will involve using the Nonresident Spouse Treated as Resident election. Your wife will be treated as a resident alien for all of 2016. As a resident alien, her worldwide income is subject to US tax, and will need to be reported on the tax return, but she should be able to use the Foreign Earned Income Exclusion to exclude the first about $100k of her foreign earned income, since she was outside the US for virtually all of the year. If she doesn't already have a Social Security Number, she will have to apply for an ITIN together with filing of the tax return.
Note that you could also file separately at first, and then (within 3 years) amend the tax return to file jointly when it is more convenient (e.g. after she gets a Social Security Number, so she won't have to go through the hassle of applying for an ITIN while abroad).