The former champion had three falls in his last four races over jumps.
Constitution Hill will not run in the Champion Hurdle at next month's Cheltenham Festival.
The nine-year-old made an impressive flat debut at Southwell last Friday.
But after three falls in his last four races over jumps, trainer Nicky Henderson confirmed that the former champion will not be part of the field.
Henderson also confirmed that he will only run on the flat from now on.

Tuesday Morning Sports Update
All Ireland Football Championship Opening Round Fixtures Confirmed
Tommy O'Brien Among Injury Doubts For Leinster's Champion Cup Final On Saturday
Monday Morning Sports Update
Sunday Evening Sports Update
Mourinho's Benefica Go Unbeaten but Miss Title
Brave Kildare Fall Short in Leinster Ladies Final
Chelsea Appoint Xabi Alonso as New Manager