The argument started when an 18-year-old youth sitting in economy class moved his seat back to sleep.
The 38-year-old passenger sitting immediately behind him was about to eat his in-flight meal at the time.
When he asked the youth to put his seat back up while he ate a major row broke out.
They traded insults and leapt up from their seats in a head-to-head confrontation.
As the argument became more heated cabin crew were called and attempted to defuse the incident.
Stunned travelers watched on as the two men continued to shout abuse at each other while standing in the aisle before they were finally persuaded to calm down.
Officers went to the gate at Terminal 1 after the flight landed to meet the two passengers at around noon on Tuesday.
A spokesman for Greater Manchester Police confirmed officers “spoke to” two men aged 38 and 18.
No further action was taken as neither man wanted to make a formal complaint, and also admitted they had both been “in the wrong”, say police.
A spokesman for Emirates said: “Emirates does not tolerate this kind of behaviour from passengers and safety will not be compromised.”
They confirmed there had been an “altercation” on board the flight and, although no blow had been exchanged, cabin crew had been called to calm the passengers.
One traveller, who uses the route, said: “I have recently flown with Emirates to the Far East. This trip was split up into 2 separate flights and lasted 20 hours.
“Like a lot of people on the second leg of the trip I wanted to sleep. There is a system in place where you can indicate that you do not want the meal and to be left alone to sleep, which is what I did. My seat was reclined to the limit allowed.
“When it came time for the meal I was woken up by the person behind asking me to sit up, so they could enjoy their meal. I was a little p***** off that I had been woken up.
“I hadn’t reclined it whilst he was eating, I was doing what I wanted to do, sleep, in a position that the seat was allowing me. I didn’t make a fuss and accepted it.
“This is only a problem in the <<cheap>> seats and perhaps the airlines can have an area in this class for passengers who want to sleep in the reclined position.
“No meals would be served to these passengers, so the problem will be removed. By sitting in this area you accept no meals and the seat in front may be reclined.”
The double-decker plane first started flying into Manchester Airport in September 2010 after around $15 million had been spent on changes to the airfield to accommodate it.
Its introduction was part of a huge boom in the number of people flying in and out of Dubai.
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