The 21-year-old has yet to feature this season because of a knee injury suffered during a training session.
As a result, Barca have allowed him to join their Dutch counterparts in order to regain his fitness and match sharpness.
"I'm very happy with him. He's a more than welcome addition to our team," manager Frank de Boer told the club's official website. "We're still competitive in three [competitions] and a player of the calibre of Cuenca is always useful. He is a very smart player and fast, he can play on the left and right wing, and besides that he's a very good football player."
Cuenca added: "After I started to train with the group, I had a little relapse. But now I feel good, ready to play.
"I'm going to have minutes [to play] and test myself after so many months of being injured."
The attacker has made 16 appearances in total for the Catalan club, scoring two goals.