The most common and most likely answer to this crossword clue is the 6 letter word GRAZES
I've seen this crossword clue in The Daily Telegraph
G
R
A
Z
E
S
More clues leading to the result GRAZES
Buddy explains!

The straight part
We know that "Minor injuries" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case minor injuries = grazes.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 GRAZES mean?
GRAZES noun- The act of grazing; a scratching or injuring lightly on passing.
- A light abrasion; a slight scratch.
- The act of animals feeding from pasture.
- To feed or supply (cattle, sheep, etc.) with grass; to furnish pasture for.
- To feed on; to eat (growing herbage); to eat grass from (a pasture)
- To tend (cattle, etc.) while grazing.
- To eat periodically throughout the day, rather than at fixed mealtimes.
- To shoplift by consuming food or drink items before reaching the checkout.
- To rub or touch lightly the surface of (a thing) in passing.
- To cause a slight wound to; to scratch.
- To yield grass for grazing.