Some of the weapons were discovered when officers stopped two vehicles in Ratoath - the same village where a man was shot dead on Wednesday night.
Two assault rifles and ammunition were found in the vehicles and in follow-up searches nearby two pistols, silencers and more ammunition was recovered.
Police said the operation is ongoing.
It involved officers from the Drugs and Organised Crime Bureau, supported by national police units, including the Emergency Response Unit.
The investigation follows the fatal shooting of Noel Duggan in The Old Mill housing estate in Ratoath at about 19:45 local time on Wednesday.
Mr Duggan was a well-known criminal linked to cigarette smuggling and also had connections to a Dublin family who were caught up in a fatal feud in the city last month.
A police statement said Thursday evening's operation was targeted at "organised criminal groups involved in the provision and distribution of firearms".
The men who were arrested are in their 30s.

The verdict threatens Apple's ability to offer its voice-controlled virtual assistant, Siri, in the country.
Shanghai-based Zhizhen Network Technology has sought to block Apple from selling products with the app installed, saying it infringed its rights.
Apple said it would pursue an appeal with the Beijing Higher People's Court.
"Apple believes deeply in protecting innovation, and we take intellectual property rights very seriously," said a spokesman.
"Apple created Siri to provide customers with their own personal assistant by using their voice.
"Unfortunately, we were not aware of Zhizhen's patent before we introduced Siri, and we do not believe we are using this patent.
"While a separate court considers this question, we remain open to reasonable discussions with Zhizhen."
The Chinese company could not be reached for comment.
Zhizhen offers its own voice-controlled service, named Xiao i Robot, which began life, in 2003, as a text-based chatbot that ran on others' instant-messaging tools.
It later evolved into call-centre software used by the Chinese government and several companies.
In addition, Zhizhen developed voice-controlled software for smart TVs, cars and smartphones - including an iPhone app that allows users to find restaurants, train times and stock prices.
In June 2012, Zhizhen accused Apple of intellectual property infringement after the US company announced at its developers' conference that Mandarin and Cantonese were being added to the list of Siri's supported languages.
Zhizhen noted that it had filed for the intellectual rights to the underlying technology in 2004 and had been granted the patent two years later.
Apple countered that Siri used a different process to power its voice-recognition tech - a court has yet to rule on this claim.
Apple also sought to block the case by asking China's State Intellectual Property Office to invalidate the patent, but was refused.
It then challenged that decision, suing both the patent authority and Zhizhen - but was thwarted on Tuesday when Beijing's Number One Intermediate People's Court ruled against it.
The China Mobile Internet Industry Alliance previously told the Xinhua news agency that it did not believe the case would result in Apple pulling its products from China, but added that the US company might have to seek a financial settlement.
Three men have been arrested after police seized guns and several hundred rounds of ammunition in County Meath in the Republic of Ireland.
[NEXT_CONCEPT]
Apple has failed in its attempt to get a Chinese company's voice-recognition patent ruled invalid.