Smith was arrested and questioned last week by police investigating the incident in which he threw a plastic bottle into the crowd.
Lawyers from the Crown Prosecution Service (CPS) said today they had now advised police not to charge Smith with a criminal offence as it would not be in the public interest.
"Area lawyers decided that there was insufficient evidence to provide a realistic prospect of securing a conviction in respect of any potential Public Order Act or assault charges," said Neil Franklin, chief crown prosecutor for the CPS in West Yorkshire.
"Whilst due weight was attached to the potential impact on, particularly younger, members of the public of Mr Smith's alleged conduct, account was equally taken of a number of other factors.
"These included the fact that there was no evidence of any premeditation on Mr Smith's part, rather that his reaction was instinctive. It was also clear that he was genuinely contrite and that he had never previously been in any kind of trouble with the police."
The FA, which had previously declined not to act until the police investigation had been concluded, will now refer the matter to its compliance unit.
If Smith is charged and found guilty he faces a potential three-match suspension.