The Spanish pair were drawn together in the last-eight stage last week and will contest the first leg at the Camp Nou on April 2.
It is understood that Barcelona have set a price of £78 per ticket, which has drawn criticism from the capital outfit's official supporters group.
"During times of economic hardship, it's a shame that fans are unable to attend the stadium for a Champions League quarter final just because ticket prices are high," a statement read.
"Around 3,000 Atletico fans travelled to Milan and were able to gain entry to the stadium for €35 (£30). Setting high ticket prices goes against football as an event and the public."
Atletico currently top La Liga with nine games remaining.