Constantine has scored just three goals since arriving in the summer and now Town are strengthened with the return of Bayo Akinfenwa from suspension and new signing Aleksandar Prijovic.
Stuart Gray said: "I think a change of scene could do Leon good.
"We have Bayo coming back and we took a striker in on loan this week so this move will give Leon the chance to play first-team football and help Cheltenham out.
"It will also give me the chance to try and add to our own squad by bringing in a fresh face and we obviously wish Leon well at Whaddon Road."