The 2010 World Cup quarter-finalists are second bottom in the nine-team South American group on four points from five matches, having lost 3-1 away to Bolivia on Saturday, despite three weeks of preparation for the high altitude of La Paz.
"It is one of the hardest decisions I've had to take along with the board. Things did not work out as one wanted and it's a shame," Paraguayan FA president Juan Angel Napout explained after announcing the decision.
Napout, who appointed Arce last year, added: "We worked hard but there is a reality in football that is results. There is no new coach yet, we're going to take our time to search."
Arce, a 41-year-old former defender who played at two World Cups but had limited coaching experience, was appointed when Argentine Gerardo Martino quit after last year's Copa America in which Paraguay reached the final.
Paraguay had high hopes against Bolivia, who had not won any of their first five qualifiers and failed to take advantage of playing their home matches at 3,600 metres above sea level.
Arce, whose team had a bye the previous weekend, took his squad to La Paz three weeks ahead of the match at the Hernando Siles stadium looking to meet Bolivia on equal terms.
The plan failed spectacularly as Bolivia, who had lost their two previous home matches and only picked up a solitary point in a surprise 1-1 draw away at Argentina, romped to victory, even missing a penalty in the process.
Paraguay have qualified for the last four World Cups and, with Martino at the helm, reached the quarter-finals for the first time in South Africa in 2010.
The APF are acting while there is still enough time to put Paraguay back on track with 11 matches still to play in the marathon qualifying campaign that resumes in September when they face a daunting trip to Argentina.
The top four in the group will automatically qualify for the finals in Brazil, with the fifth-placed team going into a playoff against an Asian team at the end of next year.
Ecuador currently occupy fourth place on nine points from five matches, one ahead of Venezuela, who have played six.
The new coach will have a friendly against China on August 15 to prepare his team for the visit to their fierce rivals in Cordoba on September 7, a clash that has always had a special flavour for Paraguayans even if they have never won it away.
Arce is the second coach to lose his job during the qualifiers after Colombia's Leonel Alvarez was sacked last November after three matches and replaced by Argentine Jose Pekerman.