Mr Joyce was giving a speech in Perth on Tuesday when the man walked on stage and shoved the pie in his face.
A man identified by local media as the attacker later criticised the airline chief's support for same-sex marriage, which is not legal in Australia.
"I will have every intention of pressing charges," Mr Joyce said.
Police charged the 67-year-old man with giving false details after the incident, which happened in front of 500 people. He may yet face an assault charge, police told the BBC.
"On the west coast, there is very limited opportunity to have connection with national figures," the pie-wielder, identified as Tony Overheu, told the Australian Broadcasting Corp.
"From my reading, it would appear that Alan Joyce is very much part of a network trying to subvert the federal parliamentary process around the issue of marriage equality."
Mr Joyce was one of 20 company chief executives who signed a petition in March calling on Prime Minister Malcolm Turnbull to legalise same-sex marriage.
Immigration Minister Peter Dutton, the government's most prominent conservative, described the attack as "a disgrace".
"The person should be ashamed. The threats any of us receive is unacceptable," Mr Dutton tweeted.
Mr Joyce had been discussing the airline's recent decision to operate non-stop flights from London to Perth when the incident happened.
"I don't know what that was about," he said, before continuing his speech.
Qantas chief executive Alan Joyce has said he intends to press charges against a man who hit him in the face with a pie.