The passengers and flight attendants involved in an in-air skirmish on an Alaska Airlines flight are now under a federal microscope ... with the FBI looking to see if a crime was committed.

Viral video from an Alaska Airlines flight from Oakland to Portland shows a flight attendant repeatedly hitting a passenger in a window seat, telling the man to let go of the hair of the woman sitting in front of him.

The FBI branch in San Francisco tells us the Bureau "is aware of the incident and appropriate steps will be taken to determine if a violation of federal law has occurred."

Alaska Airlines tells us the male passenger from the video "appeared to be experiencing a violent medical episode that involved an ongoing physical assault against other passengers and our crew."

In the video, you see the guy chanting, screaming and rocking from side to side.

The airline says the incident happened on the tarmac and the plane returned to the gate, where law enforcement got involved. Alaska says the man has been banned from the airline "due to the nature of the physical assault."

Sounds like he may have bigger problems to worry about ... depending on what the FBI determines here.

Meanwhile, the Association of Flight Attendants-CWA is applauding the crew member for stopping "a violent passenger from continued physical assault of another passenger."

The union says the flight attendant "protected a passenger and ... stopped further escalation and injury to more passengers onboard the plane."

It will be interesting to see if the feds agree. Stay tuned ...