Darren McDonald, 40, travelled from Ballymena, County Antrim, to support his team.
At Glasgow Sheriff Court he admitting running on to the pitch after the final whistle and kicking the other man on the head or body.
McDonald was also given a three-and-a-half year football banning order.
He is currently serving a sentence in Northern Ireland and the latest jail term will begin after that ends.
McDonald was named and pictured in the media after the game that saw Hibs beat Rangers 3-2 on 21 May.
Footage from the match was played to the court and newspaper reports from the time were brought to the sheriff's attention.
McDonald was seen clearly wearing a pink T-shirt and had distinctive tattoos.
The unknown Hibs fan was on the pitch after the match and was on the ground, having been assaulted by someone else.
McDonald ran over to him and pulled his right leg back to kick him but slipped and fell backwards.
The court heard that the momentum meant his leg made accidental contact with the Hibs fan's head or body.
He then got up and ran off after the attack, leaving the Hibs fan on the ground.

Chief Rabbi Ephraim Mirvis said Mr Peres "was the greatest living example of an unshakable belief in the pursuit of peace against all odds".
Former British PM Tony Blair also paid tribute describing the Nobel Peace prize winner as "a political giant".
Mr Peres died aged 93 on Tuesday, two weeks after suffering a stroke.
He was one of the last of a generation of Israeli politicians present at the new nation's birth in 1948, serving twice as the country's prime minister and once as president.
He also won the Nobel Peace prize in 1994 for his role negotiating peace accords with the Palestinians a year earlier.
Rabbi Mirvis said Mr Peres "gave hope to millions of people" that a peace deal would be achievable.
He added: "Tragically, thus far, we have not succeeded. But from Shimon Peres we learned that we must never let go of that audacious commitment to peace, even when all around us are ready to do so."
He went on: "For those of us whom he inspired during his remarkable lifetime, we say: No matter what the future holds, your legacy lives on in the Jewish people who will never rest until we achieve our eternal dream of peace among the peoples of the world."
Mr Blair paid tribute to Mr Peres on twitter, writing: "Shimon Peres was a political giant, a statesman who will rank as one of the foremost of this era or any era, and someone I loved deeply".

The gunmen seized the compound five days ago and have been demanding the release of an opposition leader arrested last month on weapons charges.
Supporters of the gunmen have staged rallies nearby and clashed on Wednesday with police, who fired tear gas.
Mr Sarkisian urged the gunmen to "sober up" and end their "provocative" action.
In comments reported by Armenian Armenpress news agency, he said: "No problem will be solved in Armenia with the use of force, raids and hostage-taking. The resolution of the problem will be an important test for Armenia and the maturity of our society."
Mr Sarkisian said the government would act "in line with Armenia's laws" if the gunmen persisted, but he gave no further details.
The hostage-takers have been demanding the release of Jirair Sefilian, a military veteran of Armenia's conflict in Nagorno-Karabakh, who has been accused of illegally possessing weapons and preparing to seize government buildings.
In taking control of the police station in Armenia's capital on Sunday, the gunmen killed one police officer and injured two others. They later released five hostages.
Those still being held include a deputy police chief.
Mr Sefilian has criticised Mr Sarkisian over his handling of the conflict involving pro-Armenian separatists in the Nagorno-Karabakh region.
Nagorno-Karabakh lies within Azerbaijan but has an ethnic Armenian majority. A bloody war erupted after the end of Soviet rule in 1988, and there has been frequent unrest since, the latest in April, when clashes left dozens dead.
A Rangers supporter who kicked a Hibs fan during a pitch invasion at last year's Scottish Cup Final has been jailed for nine months.
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The chief rabbi of the UK and Commonwealth has paid tribute to former Israeli PM Shimon Peres, describing him as a "true giant amongst men".
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Armenia's President Serge Sarkisian has urged gunmen holding four hostages at a police station in Yerevan to free their captives and lay down their arms.