The four were arrested after a major operation by the Garda Special Detective Unit at 7pm on Tuesday outside a gun dealer's premises, The Tackle Shop, at Rahan, near Tullamore in Co Offaly.
Gardai welcomed the operation as it has emerged that there were 250 shotguns and handguns in the The Tackle Shop, which is run by local man Jim Griffin. "If these weapons ended up on the streets, it could have caused mayhem," a source said.
The arrests followed a lengthy surveillance operation. Detectives seized a stolen van, balaclavas, wigs and gloves.
The four suspects are being held at various garda stations in the midlands.
Ms Shannon was previously arrested for public order offences after an anti-NAMA rooftop protest at Anglo Irish Bank in Dublin city centre on May 15, 2010.
She was also a prominent protestor during Queen Elizabeth's visit to Dublin last year. Also in garda custody today is John Troy (30), from Donard Avenue, Cabra.
Troy was one of seven men who were convicted and jailed for four years in February 2005 after they were found acting suspiciously in Bray, Co Wicklow, in October 2002.
During their trial the Special Criminal Court heard that the men were arrested after an off-duty Special Branch detective noticed suspicious activity around three vehicles -- a Nissan Almera car, a Nissan Micra car and a van.
The court heard that gardai recovered election posters for Sinn Fein TD Aengus O Snodaigh, from the Nissan Almera car in which they also found a stun gun, a CS gas canister, a blue flashing light and a beacon.
Gardai also found two pick-axe handles, a lump hammer, three portable radios, cable ties, balaclavas and a fake garda jacket in the van, and four of the men were found seated on the floor of the van. Two of the men -- not Troy -- were dressed in fake garda uniforms.