Kumar, who pleaded guilty at a post-play hearing, couldn't hide his frustration after an lbw appeal against England's Kevin Pietersen was turned down by South African umpire Marais Erasmus in the 18th over.
There are no lbw reviews this series because of Indian objections to ball-tracking technology.
But that didn't stop an angry Kumar questioning Erasmus at the end of the over before being pulled away by team-mate Harbhajan Singh.
Kumar was found to have breached Article 2.1.3 of the International Cricket Council (ICC) code of conduct which relates to arguing or entering into a prolonged discussion with the umpire about his decision.
But because Kumar, who led India's attack with three for 45, pleaded guilty and accepted Sri Lankan match referee Ranjan Madugalle's verdict, there was no need for a formal hearing.
Pietersen was eventually dismissed for 22 in an England total of 221.
India closed on 24 for one, a deficit of 197 runs, as they looked to level the four-match series at 1-1.
