Sleeping in airports is generally frowned upon in all Japanese
airports. While the terminal is open, you will likely be approached by
a security officer who will ask to see your travel documents
It also links to a quote from the Narita website, although I can't find the quote on that page.
Aircraft operating hours is between 6:00 a.m. and 11:00 p.m..
Customers are not permitted to remain in the passenger terminals
outside aircraft operating hours. However, under special
circumstances, for example when an aircraft arrives after public
transport stops operating, customers may be allowed to sleep in
designated areas. Moreover, customers catching early morning flights
are advised to use nearby hotels and accommodations around the
It does however say that sleeping facilities can be reserved in advance in the day rooms.
From some of the comments, however, on sleepinginairports, some had no problems and even had the police show them comfy places to nap. So it looks like officially, no, you can't, but in reality depending on your luck, you may be able to.