The 19-year-old has made two substitute appearances for the Eagles in the Capital One Cup this season, against Walsall and Newcastle United.
He will go straight into the Robins' squad to face Morecambe at home on Friday night (7.45pm).
Palace signed Aylesbury-born Gray from Wycombe Wanderers in the summer of 2012.
He can play across the midfield and is likely to be used in a right midfield role during his time with Cheltenham.
"I like Jake and he has scored four goals in 10 appearances for Palace's development team this season," boss Paul Buckle said.
"He's been on our radar for a while and he fits in with the financial structure at the club."