Team-mate Nico Rosberg was forced to retire on the first lap after being hit by another car.
Michael ran a two-stop prime/option/option strategy, stopping on laps 17 and 36. His strategy made full use of his two available new sets of option tyres to gain 12 positions.
In the final stint, he caught the cars ahead of him at over a second a lap but was unable to pass for P10.
Nico was eliminated by a collision in turn two when he was hit from behind by Bruno Senna's Williams.
Michael Schumacher: "I have mixed feelings after the race here in Japan, because it's obviously unfortunate to come so close to scoring points and not manage it, after a race which went better than we expected.
In the final laps, I had a nice and interesting battle with Ricciardo, but in the end I couldn't get past him because the Toro Rosso was so quick on the straights.
That's why we have to say we couldn't have got much more out of it today. Now let's see how things go in Korea."
Nico Rosberg: I had a good start to the race but unfortunately it ended fairly quickly today. In the first corner Grosjean spun into Webber and that also led to my accident.
I began to brake but Senna crashed into me from behind which destroyed my rear tyre and meant that I had to retire.
It's a shame as I felt very comfortable with my car on the installation lap, and I was confident that we could score some decent points. I'll now hope for a better weekend in Korea.
Ross Brawn: "From where he started today, Michael drove a strong race, and it's a shame that he didn't get some points for his efforts.
However starting from 23rd on the grid made that just too much of a challenge, despite a very good strategy and encouraging pace from the car in the lower temperatures.
The accident which caused Nico's retirement was a great shame as the car was in good shape and he could have scored decent points if he hadn't been taken out.
There were some encouraging signs in the race and we will take heart from that as we continue to work on improving the car.
Norbert Haug: A good performance and a good drive from Michael during the race, which saw us posting good lap times for the first time this weekend - and Michael setting the sixth fastest lap time around three-quarters of the way through the race.
After starting P23 following his ten-place grid penalty, Michael came home in P11, chasing the car ahead during the last seven laps. He caught him quickly, setting better lap times in the final stint, but in the end he unfortunately could not overtake to score the flast available point.
Nico was eliminated during the first corner crash through no fault of his own, so no points today for him or our team. We are now looking forward to the race next weekend in Korea.
Source: Mercedes AMG Petronas