The short answer is maybe.
According to the Hanafi school of thought, bleeding breaks wudu only when the impurity exits and flows/spreads from its original place on to the skin. If blood becomes visible at the wound but does not move away from that spot and does not spread, your wudu does not break.
This applies so long as the impurity is not from the two private parts. That would automatically invalidate wudu regardless of whether it "flows" or not.
Examples: Bleeding & Wudu
Hafsah grazes her arm. She can see blood where the graze is, but no blood flowed out. Her wudu has not broken.
Reason: The blood did not move from its original position or spread on the skin.
A small graze with a red shine at the spot but no trail on the skin: Wudu intact.
Reason: blood visible but did not spread.
A cut where blood travels beyond the cut and leaves a mark on the surrounding skin. Wudu is broken.
Reason : Blood exited and flowed.
How to Check your Wudu when you Bleed (Hanafi)
Ask yourself two main questions:
- Where did the bleeding come from? If it came from the two private parts this breaks wudu automatically. If this is not the case, then ask question 2.
- Did it exit and flow? If the blood exits and flows/spreads from the wound onto the adjacent skin then wudu has broken
Key definition (Hanafi): Wudu will not break until the impurity “moves away from its original position (i.e., wound site) and flows onto the skin.”