Nov.4 (GMM) Kamui has apologised after photographs emerged of him smoking a cigarette.
The former Toyota and Sauber driver, who is hoping to return to the grid, now races GT sports cars for Ferrari.
But his bid to return to the F1 grid was dealt a blow when the popular Japanese gossip magazine 'Friday' published photos of him walking on a street at night with an unidentified beauty and a cigarette.
Kobayashi, 27, admitted that his behaviour was "inappropriate for a sportsman".
"I sincerely apologise to those who gave me your support and all of my fans who were concerned," he is quoted as saying.
Kobayashi admitted that smoking was "a very thoughtless act" for someone "working towards returning to F1".
"I guarantee that this situation will not happen again," he promised.