The 26-year-old forward joined the Citizens in the summer of 2008 from Real Madrid for a British record fee of £32.5million, but has struggled to make his mark in England.
He had previously moved to Europe from Santos in the summer of 2005, but decided to leave the Bernabeu after three seasons with the Spanish giants.
In total he has scored 16 times in 53 appearances for City, but only one of those strikes has come this season.
Manager Roberto Mancini told the club's official website: "Robinho is someone who needs to be playing regularly and we wish him well for the period of his loan."
Robinho had previously told Brazilian TV network Globo: "Santos want a year but City want just six months.
"Here Mancini said that I would play one game and another no. I didn't accept that and told him so. It's a World Cup year.
"The directors all agree that it's better to send me out on loan. It would be exceptional to return to Santos.
"Playing for Santos would help me in my path to the World Cup. It is my home, I know everyone."