SFO Spokesman Doug Yakel said officers responded to a call of a person acting suspiciously along the lower level roadway outside Terminal 1, which serves Southwest and Delta airlines.
The person had gone inside one of the baggage claim areas by the time officers arrived.
When the officers confronted the man, he allegedly stabbed one of the officers in the leg.
Yakel said the wound did not appear to be life-threatening and the officer was transported to San Francisco General Hospital.
The baggage claim area was being treated as a crime scene while police investigated.
The suspect was taken into custody.