Mr Correa announced the move in a letter to President Juan Manuel Santos of Colombia. He called Washington's veto of Cuban participation "intolerable", saying its exclusion was not by consensus.
US President Barack Obama is among regional leaders due to attend the summit, held every three years.
"After some reflection I have decided that while I am the president of Ecuador, I will not attend any Summit of the Americas until it begins to make the decisions required," Mr Correa said in his letter.
"There has been talk of lack of consensus, but we all know that this is the veto of foreign powers."
So far, Mr Correa is South America's only leader to confirm he will not attend the meeting, which opens in Cartagena on 14 April.
He proposed last month that the presidents of the leftist Bolivarian Alliance - which includes Venezuela, Bolivia and Nicaragua - all boycott the summit. However, the presidents of all three nations have since confirmed they will attend.
President Santos announced last month that Cuba would not be invited, following talks with Cuban President Raul Castro in Havana.
Washington says Cuba should not be allowed to attend as it is not a member of the Organization of American States (OAS), which backs the event.
Story courtesy of the BBC