The deal does not include an option to buy Piazon, who turns 19 on Sunday and has a contract with the English Premier League side and European champions until 2017.
"(Coach) Manuel Pellegrini can deploy him for Malaga CF in the UEFA Champions League as he was registered and even on the bench for Chelsea during the competition but was not used," Malaga said in a statement on their website.
Sao Paulo-born Piazon made his Chelsea debut in September in a Capital One (League) Cup match against Wolverhampton Wanderers and first appeared for the club in the league in last month's 8-0 win against Aston Villa.
He helped Chelsea win the FA Youth Cup last season and was voted the club's Young Player of the Year.
He will give Pellegrini an extra attacking option in midfield as they seek to advance past Porto to the quarter-finals of the Champions League on their debut in Europe's elite club competition.
Malaga are fifth in La Liga after Sunday's defeat at home to unbeaten leaders Barcelona and play at Barca later on Wednesday in a King's Cup quarter-final first leg.
Piazon has not travelled with the rest of the squad and will be presented at the club's Rosaleda stadium on Thursday, Malaga added.