The "Detailed Tables" from the ACS (i.e., the ACS Summary Files) include "geographic components" that allow you to breakdown data for certain levels further by metro / non-metro / micropolitan / urban / rural and a few other geographic subcategories. The set of available level-component combinations is listed in the "Appendix B" sheet in the Summary File Appendices, accessible through this page. That shows that you can get data for people "in metropolitan statistical areas" by state for the 1-year tables.
You could extract these data from the raw summary files, but they're a bit bulky. And unfortunately, as far as I can tell, there's no easy way via data.census.gov to get data for a single geographic component for all states at once. It seems you'd have to click on a separate box for the component of interest once for each of the states. (Ugh.) (EDIT: I now see that Glenn Rice pointed out the same problem in another response... so it's not just me that can't find another way to do this!)
Fortunately, we make it pretty easy (IMO) to get this type of data via IPUMS NHGIS. Through the NHGIS Data Finder, I'd select a "Geographic Levels" filter for "State", and then select a Years or Datasets filter for the ACS year I'm looking for. Then find and select the table of interest (in this case, B01003. Total Population), continue to the Options page, and there I can select which "spatial breakdowns" I'd like to include in my data request. I'd select the breakdowns for "Total area" and "In metropolitan statistical area" and continue on to request and download the data. Then I can get state-level total population and population in metro areas in one file, and just divide one by the other to compute the share.