I wouldn't say that the FPS is unpopular in Japan in the sense that Japanese gamers actively dislike/avoid them, given
Call of Duty and Battlefield have sold decent numbers there(and the Metroid Prime games have also done decently). Instead, I think it's the old chestnut of western games generally being less popular in Japan, and FPS's being a predominately western-developed genre. There are a few things I'd like to expand on:
First, in the same way that many JRPGs aren't released outside Japan, many western shooters won't be released in Japan. Call of Duty is published by Square Enix there, so what hope for smaller titles whose publishers may or may not justify the expense of localising and distributing a game where it's likely to not sell. The previous president of Sqaure, whose name escapes me, was well known to be a fan of western games and made efforts to actively promote them in Japan. He was, however, in a minority, so it's easy to see how general apathy could set in among publishers and, in turn, players.
Second, the two platforms which have arguably done most in shooters' development, PC and Xbox, have a far smaller market share than in the west. In other words, while the likes of Doom, Half-Life and Halo were wildly known and very popular in the west, they would have niche appeal at best in Japan. This leaves PlayStation (and Nintendo, albeit to a far lesser extent) consoles, which have a far less glamorous history.
Combine these two factors, and it's conceivable that many Japanese gamers' first exposure to the FPS would be Call of Duty on the PS3, as localised by Square. The formative shooters we take for granted will have had little exposure due to their platforms, and so it's a lack of history, as opposed to player dislike/disinterest/whatever, which explains why the FPS is less popular in Japan.