Onana had played in Cameroon's opening game at the World Cup, a 1-0 loss to Switzerland, but was dropped for the Serbia game and didn't travel with the rest of the squad to Al Janoub Stadium. Cameroon fought back from 3-1 down to draw 3-3 without its No. 1 goalkeeper.
Song said it was a risk to play with reserve goalkeeper Devis Epassy but insisted he had to take "strong action" against the 26-year-old Onana.
"If you can't fit in with what's required to be part of a squad then I do think that you need to step up to the plate and accept responsibility for that because the team, the squad, is more important than the interests of any individual," Song said Monday after the Serbia game without going into details of his disagreement with Onana.
Song said he needed all his players to "show discipline and respect."
In his statement, Onana said he was disappointed that he was "not allowed" to be with the team at the Serbia game and denied that he had broken any squad disciplinary rules.
"I always behaved in a way to lead the team to success in a good manner," Onana said.
Cameroon still has a chance of qualifying for the last 16 at the World Cup but needs to beat top-ranked Brazil in its final Group G game and hope that the result of the Switzerland-Serbia match goes in its favor.
Song is a former captain of Cameroon who was appointed coach in February in a surprise to some after Toni Conceicao guided the team to third place at this year's African Cup of Nations and only missed reaching the final in a penalty shootout loss to Egypt.
The president of the Cameroon soccer federation is Samuel Eto'o, a former teammate of Song on the national team.