Dorset Police were called to an address in Hinton Road just after 2pm.
The man was taken to hospital for treatment.
Police said his condition was unknown.
No arrests have been made yet.
A Dorset Police spokesman said: “Dorset Police received a report at 2:11 pm on Thursday 14 July 2022 that a man had been found with stab wounds to his leg at an address on Hinton Road in Bournemouth.
“The man was taken to hospital for treatment.
“We don’t have a condition update at this time.
“Agents have been on the scene and are investigating.
“No arrests have been made at this time.”
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