No, you can't.
thanks - good to know
check www.wmata.com for all your metro questions
If you're a Civil War fan, I wouldn't be so quick to dismiss the idea of renting a car for a day to make the trip--not only to this museum (which is excellent), but to other historic Civil War-era sites in the general direction.
Frederick is about an hour from Arlington, and Reagan Airport is very close to your hotel with plenty of rental car choices--shouldn't cost you any more than $40 and you won't have the hassle or expense of parking it locally. If you want to expand your visit beyond the museum--from Frederick, Gettysburg would be about 45 minutes, and Antietam Battlefield and Harpers Ferry, WV would be about 30 minutes. Monocacy Battlefield is along the way to Frederick.
Depending on your level of interest in Civil War medicine, you might also enjoy the Clara Barton National Historic Site. While much closer to DC, that too is largely inaccessible if you don't have a car.
No need to split hairs, guys. It really doesn't matter in the context of the question asked by the OP.
Frederick is the second-largest incorporated area in the state, after Baltimore. Areas like Columbia and Germantown are not incorporated as cities. They have larger populations, yes. But really, does this matter for the OPs question about visiting Frederick?
Not that I would recommend it in this case, but just for everyone's future information, MARC trains DO provide weekday service between DC and Frederick, for visitors willing to lodge 2 nights in Frederick to accommodate the train schedule: see http://marc/schedule.SystemMapsEdited: 10 November 2012, 00:18
correction -- that's http://mta.maryland.gov/marc-trainEdited: 10 November 2012, 00:22
http://www.medicalmuseum.mil/ National Museum of Health and Medicine seems to have reopened, at its new location in Silver Spring. We went when it was on the grounds of the Walter Reed Army Medical Center, and it had exhibits on Civil War era medicie. Even the bullet that killed Lincoln, as I recall. Getting there by Metro wouldn't be easy. It's a mile from the Forest Glen Metro station. The WMATA Web site should give you info on buses from there.Edited: 11 November 2012, 12:21