More than 20 people have died from the H1N1 virus in Costa Rica.
Last month, Arias brokered talks to try to end a political crisis in Honduras after Manuel Zelaya, president, was ousted in a coup on June 28.
Negotiations broke down two weeks ago over whether Zelaya can return to power and Arias's illness is unlikely to affect the situation in Honduras.
While the vast majority of H1N1 cases have not been serious, infected people who have other medical conditions are most susceptible to complications.
Arias suffers from asthma, but officials have dismissed any concerns.
"The tests ... show that there is no other complication," Mayi Antillon, Costa Rica's information minister, said.
The World Health Organisation declared the H1N1 outbreaks a pandemic on June 11.
The H1N1 flu outbreak has spread around the world since emerging in Mexico in April and could eventually affect two billion people, according to the WHO.
The number of deaths from the virus in Brazil, South America's largest country, rose to 132 on Tuesday, Jose Temporao, the country's health minister, said.
If confirmed by the WHO, the new toll would mean Brazil has overtaken Mexico to become the country with the third largest number of fatalities after the US and Argentina.
The bulk of the victims died in southern Brazil, where southern hemisphere's winter is at its peak.