The 28-year-old, one of four first-choice players born or brought up abroad, swore and kicked a water bottle when he was taken off in the 93rd minute just as he was preparing to take a free kick.
"My emotions were all out of control because of the match, that was what caused my reaction. It was a very bad reaction and I apologise for it," the FA's website quoted Obraniak as saying.
Coach Franciszek Smuda told reporters on Wednesday that the matter was already done with.
Polish media have speculated that Obraniak will be dropped against the Czech Republic on Saturday in favour of Adrian Mierzejewski, who came on against Russia, in a bid for more creativity up front.
The hosts have struggled to create more than a handful of half chances in two draws so far at the tournament and must win for the first time ever at a European Championship finals against the Czechs to reach the quarter-finals.
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