The 22-year-old Shakhtar Donetsk player denied using the substance, which is a diuretic.
"I have never used any illicit substance," he said in a statement. "I trust in my innocence and I am going to prove it to the proper authorities. I have a clean career and I have everyone's support."
A surprise choice for the squad, Fred started Brazil's first two games, a 2-1 win over Peru and a 1-0 loss to Colombia.
However, he was dropped for the third match, a 2-1 win against Venezuela, and also missed the quarter-final penalty shootout defeat by Paraguay.
In a confusing statement, the CBF said they had sent organisers a list of the medicines Brazil was taking to the tournament and that the banned substance was not on it.
However, they did not say whether Fred could have taken it without the authorisation of the team doctor and they gave the player only qualified backing.
"The medical department is on hand for the competent authorities with the player's medical forms and documents if they are required," the CBF statement said.
"We stand with the player and, if needed, his advisers and lawyers can offer more explanations."
Shakhtar included Fred in the lineup for their Champions League third qualifying round first-leg tie at Fenerbahce on Tuesday despite being advised by UEFA not play him.
Fenerbahce lodged a protest with by European soccer's governing body after the game, which ended 0-0.
UEFA is investigating the matter and will announce a decision on Monday, according to a letter from the ruling body published on Fenerbahce's website (www.fenerbahce.org).
The sides are due to meet in the second leg on Wednesday with the winners advancing to the playoff round for a place in the group stage of the lucrative tournament.
(Reporting by Andrew Downie; Editing by Ken Ferris)
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