The two men, who were arrested on Monday, "exercised their right not to speak", and the judge granted them conditional release while the investigation continues, the Barcelona court said in a statement.
Bartomeu resigned in October, avoiding a vote of no confidence triggered after more than 20,000 club members signed a petition against him.
His departure came in the same month Barcelona announced losses of 97 million euros ($114 million) for last season and following a dramatic decline in performances on the pitch as well as a personal falling-out with Messi.
The operation comes less than a week before presidential elections are to be held at the club.