Michael Fitzpatrick, 30, held his three-year-old son in one arm while using the other to grapple from out of the crowd at the Europa League tie between Everton and Lyon at last year.
He was jailed for eight weeks after he pleaded guilty to assault when he appeared at the Community Justice Centre in Bootle, Merseyside Police said.
Fitzpatrick, of Prescot, Merseyside, was also given a six-year football banning order due to the serious aggravating factor of the assault taking place while holding a child.
The footage of the incident at Everton’s Goodison Park stadium last October went viral.
It took place in the 63rd minute of the match after Everton’s Ashley Williams barged into Lyon keeper Anthony Lopes.
Wearing a tracksuit, Fitzpatrick could be seen in TV pictures striding to the front of the Howard Kendall Gwladys Street End.
He then aimed punches as players grappled near the touchline.
Superintendent Dave Charnock said: “The majority of fans went to the game to enjoy it for what it was – a football match between two passionate clubs.
“The police will not tolerate the selfish and idiotic actions of a few attempting to spoil a game of football that the vast majority of people went along to enjoy.”
Mr Charnock added that the father will now have a criminal record.
He continued: “We will continue to work closely with all of our local clubs to make matches safe and enjoyable occasions for everyone, and ensure that we look to prosecute anyone who commits this type of behaviour.
“Fitzpatrick will now will have a criminal record and the consequences of this in the future could be significant.”
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Everton banned Fitzpatrick from Goodison Park for life after the incident.
Fitzpatrick later said he felt “ashamed” at his behaviour and feared his former partner will ban access to their children as a result of what happened.