The most common and most likely answer to this crossword clue is the 5 letter word BIRCH
I've seen this crossword clue in Financial Times
B
I
R
C
H
Buddy explains!

The straight part
We know that "made of wood" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case made of wood = birch.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does BIRCH mean?
BIRCH noun- Any of various trees of the genus Betula, native to countries in the Northern Hemisphere.
- A hard wood taken from the birch tree, typically used to make furniture.
- A stick, rod or bundle of twigs made from birch wood, used for punishment.
- A birch-bark canoe.
- To punish with a stick, bundle of twigs, or rod made of birch wood.
- To punish as though one were using a stick, bundle of twigs, or rod made of birch wood.