The most common and most likely answer to this crossword clue is the 6 letter word AMNION
I've seen this crossword clue in The Guardian
A
M
N
I
O
N
More clues leading to the result AMNION
Buddy explains!

The straight part
We know that "Baby wrap" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case baby wrap = amnion.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 AMNION mean?
AMNION noun- The innermost membrane of the fetal membranes of reptiles, birds, and mammals; the sac in which the embryo is suspended.