Players are not allowed to seek direction on reviews apart from conferring with the non-striker. Teams cannot make more than two unsuccessful review requests per 80 overs.
Smith, who sought help after being judged leg before wicket, said it was a one-off incident caused by "brain fade" but Kohli countered that it was not the first time it had happened and that he had complained to the match officials.
Kohli's public criticism of the visitors could have also been considered a breach of ICC code of conduct.
"In relation to Steve Smith and Virat Kohli, the ICC has considered both incidents in the context of this match and concluded it will be taking no further action against either player," the governing body said in a statement.
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The third test between the teams starts in Ranchi on March 16 with the series level at 1-1.
"Ahead of (the third test), the match referee will bring both captains together to remind them of their responsibilities to the game," ICC chief executive David Richardson said.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Pritha Sarkar)
