While it won't be the most efficient or direct routes, flights would be redirected South of Russian airspace.
They're probably avoiding Ukrainian air space too, just to be on the safe side. A quick browse of Eastern European airspace on FR24 confirms a large hole in tracked traffic over Ukraine at this time.
Thanks to tml's comment, here is a map image of the Lufthansa flight he noted.
Another option would be to go North across the North Pole instead of East. Based on this Great Circle map from Amsterdam to Narita, the GC distance would be 5805 miles. However, adding in Fairbanks to get it to go the other way increases the distance to 7720 miles.
I'm not sure what airports are along the way via the southern route to force a GC map down south, and there would probably be several options. I would imagine though, that a more southerly route is still going to be shorter.
Heading further south to avoid China, should that become necessary, I chose Ho Chi Minh City as a stop between Amsterdam/Schipol and Narita. That route ends up being 8848 miles and the GC route still crosses Western China, so the actual route would be even further, making the "fly East to go West" option a better one.
- AMS-NRT: 5805 miles
- AMS-FAI-NRT: 7720 miles. An increase of 1915 miles or 33%.
- AMS-SGN-NRT: 8848 miles. An increase of 3043 miles or 52%.