Brazilian Piazon, 18, has played only three times since signing from Sao Paulo last January, making two appearances in the Capital One Cup and one in the Barclays Premier League.
"We have an agreement with Malaga for Lucas Piazon to go on loan there until the end of the season," interim Chelsea boss Rafael Benitez said.
Benitez has ruled out recalling Romelu Lukaku, 19, from his successful loan spell at West Brom, where he has scored nine goals in 22 matches since August.
"Romelu went there as a young player and he's doing well. He's getting experience in the Premier League," he said.
"You never say never because you might have a problem, but at the moment the idea is that he stays there and gains more experience."