Royal Parks says it happened sometime between the 12th and 16th of this month.
The recently planted tree was an 8ft Toona Sinensis Flamingo, known as a Chinese Cedar.
Although not rare, it is said to be unusual enough to stand out, and anyone with information should call police on 101.
If you have any information call 101 and quote 01/253410/24 or e-mail BushyPark@met.police.uk