The former Toyota and Sauber grand prix racer, now part of Ferrari's GT programme, was driving the team's 2009 F60 F1 car when he lost control on the wet surface and hit the barriers nearly head on.
But that did not end Kobayashi's participation in the day as Ferrari had brought a second car and was able to resume running within 20 minutes.
"The track was very slippery and there was a marked bump at that point, which is why I hit the barrier," said Kobayashi.
"A shame, but I am pleased the team let me out again after a few minutes."
McLaren, Caterham, Lotus and DTM teams also took part in the Moscow event.