Nicknamed "el Flaco" (the Skinny one), he made his debut for the national team in an April 1991 friendly match against Mexico, collecting a total of 31 caps and scoring 9 goals. Arnáez appeared in seven of Costa Rica's qualifying matches for the 1994 FIFA World Cup, as well as two qualifiers for the 1998 FIFA World Cup. He also represented Costa Rica at the 1997 UNCAF Nations Cup and in the 1998 CONCACAF Gold Cup, playing against Cuba and the United States. Upon Alajuelense's triumph in the 2004 CONCACAF Champions' Cup, he was recalled to the national team at the age of 36 by coach Jorge Luis Pinto. His final cap came in a 2-5 loss in World Cup qualifying against Honduras on 18 August 2004.