Biggar, who scored 14 points in last weekend's 22-18 victory in Osaka, has a hamstring problem that meant he did not train with the rest of the Wales squad.
Team manager Alan Phillips said: "We will know more about selection on Thursday because we still have a few guys with a few problems.
"Dan Biggar is not training today because he has a tight hamstring. It's nothing to worry too much about but we're looking after him."
Biggar was put through his paces separately as Wales trained against the two-time Japanese champions Suntory Sungoliath.
Exeter Chiefs prop Craig Mitchell is set to be available having recovered from a previous ankle problem.
Phillips said: "We can't work the players too hard this week because it's the end of another long season. It's about looking after them for one final push, though we definitely expect them to play a lot better because it's their second game together."
It has been confirmed that there will not be a television match official for Saturday's game at Prince Chichibu Memorial Stadium.
Wales were unhappy that they had not been informed there was no video referee for last week's first Test in Osaka.
That was highlighted when they requested match referee Lourens van der Merwe to check for obstruction leading up to Japan's first try while Biggar also believed a penalty kick that was ruled wide had, in fact, gone through the posts.
Phillips said: "As we understand, tier two rugby nations do not necessarily get TMOs for Test matches because there's a big cost factor involved to fly people out from, say, Australia or New Zealand, for a couple of weeks. It was surprising but that's the ruling.
"We're not worrying too much about it because it doesn't change much. There were opportunities that could have worked either way on Saturday, it's just the way it is.
"It's part of the experience when you come to a developing rugby country and perhaps that's good for us. You can get blase about the organisation back home in the Six Nations and other games so we have to deal with it and that's not necessarily a bad thing."
Wales are unlikely to have to face the same temperatures as the 31-degree heat of Osaka having arrived to rain in Tokyo, though Phillips insists the Six Nations champions would rather dry conditions.
Phillips said: "It's cooler which makes life easier but we always want to play with a dry ball and pass it around. That's our style of game."
However, Japan insist they have taken confidence from outscoring Wales on tries and pushing their opponents so close in the narrow defeat.
Centre Male Sau said: "We created more chances than Wales and outscored them on tries but unfortunately we didn't capitalise and missed a few kicks.
"That could have made the difference but we still made a big statement for Japan rugby. We probably surprised Wales in the first game and that won't happen again so we will have to improve and come up with a few new things."