Is Michigan a Midwestern state? If yes, then why does Detroit falls under the same time zone as the New York City?

Michigan is considered Midwestern. Time zone isn't a factor in determining region, generally speaking. Some states split time zones, Indiana--Eastern and Central; Kansas--Central and Mountain, South Dakota--Central and Mountain; Kentucky--Eastern and Central; Texas--Central and Mountain; Idaho--Mountain and Pacific, just to name a few.  

Yes, we are a Midwestern state.  The time zone was chosen for political reasons which I can't pretend to understand.  Note that the 4 counties on the Wisconsin border are in the Central time zone.

So what? Ohio and Indiana are also considered Midwestern, and both use the Eastern time zone.

Time zones aren't based on what a state is considered, and don't always follow state boundaries. Part of Michigan is in another time zone (central, same as Chicago); only part of it is in the eastern (New York) time zone. I think Lake Michigan is the boundary; could be wrong.

Michigan used to be in Central Time, and in the early 20th century Daylight Saving had not been invented yet. In the summer, sunset happened at like 7pm which is pretty early. So some dudes set up a society to lobby for Eastern Time in Detroit, making summer sunsets occur at 8pm. Effectively, their goal was like a permanent DST. The rest of Michigan apparently followed suit, so that they weren't an hour off from Detroit.

People tend to think of anything west of Pennsylvania as "midwestern," and the time zone makes no difference.  I grew up in Ohio, which is just across Pennsylvania from New York and shares its time zone, but when I went east to boarding school and university, everyone regarded me as a midwesterner, even though Ohio (and Michigan) are a lot farther east then the middle of the nation is.

That's just the way people see it.

Is this a serious question?  You do realize, don't you, that states like Michigan and Indiana are at the westernmost part of the Eastern Time Zone. What are you asking actually?