The Saudi Arabia Football Federation earlier "unreservedly" apologised for the incident, which a former Australian government minister said showed "a disgraceful lack of respect" for the victims of the London attack.
"After reviewing the match report and images of the said match, we can confirm that there are no grounds to take disciplinary action in relation to the matter you mention," FIFA said in a statement.
Eight people were killed and 50 injured after three Islamist militants drove into pedestrians on London Bridge last Saturday, then attacked revellers nearby with knives. Two of the dead were Australian.
Football Federation Australia (FFA) said it had "sought agreement" from the Saudis and the Asian Football Confederation to hold the minute's silence to honour the victims ahead of the match at Adelaide Oval late on Thursday.
The Australia team duly lined up in the centre circle and linked arms but all bar one of the Saudi players dispersed around the pitch and continued to jog and stretch.
"Both the AFC and the Saudi team agreed that the minute of silence could be held," an FFA spokesman said.
"The FFA was further advised by Saudi team officials that this tradition was not in keeping with Saudi culture and they would move to their side of the field and respect our custom whilst taking their own positions on the field."
The incident prompted a social media storm, coming as it did at a time when Australians were still mourning victims of recent attacks.
In addition to the Australians who died in London, a deadly siege in Melbourne on Tuesday that Prime Minister Malcolm Turnbull called "an act of terrorism" claimed one victim, while an Australian schoolgirl was one of more than a dozen killed in a Baghdad car bomb blast last week.
Anthony Albanese, a front bench spokesman for the opposition Labor Party, said the incident was "bloody disgraceful".
"There is no excuse here. This isn't about culture, this is about a lack of respect," he told Channel 9.
"I'm so angry about this."
The governing body of Saudi football later issued a statement saying it "deeply" regretted the incident.
"The players did not intend any disrespect to the memories of the victims or to cause upset to their families, friends or any individual affected by the atrocity," it added.
"The Saudi Arabian Football Federation condemns all acts of terrorism and extremism and extends its sincerest condolences to the families of all the victims and to the government and people of the United Kingdom."
Prime Minister Turnbull said on Friday that he had not seen video of the incident but thought everybody should condemn "terrorism".
"The whole world, the whole free world, is united in condemnation of that terrorist attack and terrorism generally," he told reporters in Tasmania.
Australia won the match 3-2 to move level on 16 points in Group B with the second-placed Saudis and leaders Japan, who have a game in hand, with two rounds to play.
The top two teams win a place at the World Cup finals in Russia next year.
(Writing by Nick Mulvenney, additional reporting by Ian Ransom, Ahmed Maher and Colin Packham, editing by Ken Ferris/Peter Rutherford/Sudipto Ganguly)
