Justice Minister Alan Shatter said he was concerned about the use of the device thrown at the statue in Trim, Co Meath, almost two weeks ago on April 21.
"It is quite possible, but not certain, that it may have been some sort of atavistic response to the announcement that Queen Elizabeth is to visit the country later this month," he said.
But he insisted he had the utmost confidence in the Garda to deal with any security threat to the first official trip to the Irish Republic by a reigning British monarch.
Mr Shatter said while the government upheld the right to peaceful protest, it would not tolerate those who sought to break the law or who set out "to maim or murder".
"By their actions they display a barbaric and arrogant content for the constitutional civil and human rights vested in all who reside on or visit this island," he added.
Mr Shatter said the vast majority of the people of Ireland would welcome the Queen, as well as US President Barack Obama, when he also visits later this month.
There was a small explosion during the early morning incident in Trim, but no injuries or damage, apart from some scorch marks to the landmark.
Nobody has claimed responsibility.
Mr Shatter warned anyone convicted of explosives-related offence could face stiff penalties, including life imprisonment for causing an explosion likely to endanger life.
© Press Association