Victoria Police said the weapons were found on each of the men during a search about 8.30pm on Thursday, as a crowd of 82,058 fans watched Collingwood defeat Carlton.
Officers were asked to get involved when the pair refused a request from security to leave the venue over their behaviour, the force said.
Melbourne Cricket Club chief executive Stuart Fox said the incident was "extremely disappointing and upsetting".
"Our security screening units identified items of concern and further investigation was required," he said in a statement.
"Our initial internal investigation identified a breakdown in the thoroughness of the secondary and manual screening process."
He said the "extensiveness" of manual security at the stadium will be increased, so fans can expect delays at upcoming events.
AFL chief executive Andrew Dillon said there would be an "end to end" security review.
"The MCG worked to identify how the two men were able to enter the venue, which concluded that security personnel failed to do a thorough follow up search of the patrons after an alert from the entry point screening system," he said.
"Both patrons who were arrested last night will be issued lifetime banning notices from the AFL for attending any match."
Both men were on bail at the time.
Roxburgh Park man Omar Salam, 21, faced court on Friday morning and he was remanded in custody until his next court appearance on April 16.
He wore a white T-shirt with a black Nike logo and listened closely to Magistrate Timothy Bourke during his brief court appearance.
He was charged with being a person prohibited from possessing a firearm, possessing ammunition without licence and committing an indictable offence while on bail.
A 27-year-old man from Broadmeadows was charged with possessing an unregistered handgun, possessing ammunition without licence, altering the serial number of a firearm, possessing a loaded firearm, possessing a prohibited item and failing to appear on bail.
He is due to face court later on Friday.
Counter terrorism police were called to assess the incident but will have no further involvement, with the probe now in the hands of the crime investigation team.
Prime Minister Anthony Albanese praised the officers involved in the search and described the incident as "pretty shocking".
"Frankly, I hope that they get the book thrown at them for this and I do want to thank Victoria Police for their work in keeping people safe," he told ABC Radio Sydney.
AFL Fans Association president Ron Issko was also shocked and said nothing like this had ever happened before.
He said fans were subjected to several security measures including walking past detector pillars and individual security checks.
"If they have to make some changes this weekend to security, fans will accommodate," Mr Issko told AAP.
"I'll be going to the footy this weekend and I've got all the confidence in the security and the police at the footy."
He said any security upgrades must be done urgently.
"Ninety-nine per cent of fans are great. If we've got some ratbags let's get rid of them," he said.
The MCG underwent a security upgrade in 2024 including the roll out of artificial intelligence sensors, called Evolv Express.
"Evolv Express uses sensors combined with AI to differentiate between weapons and common metals people carry," according to the company's website.
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