The 45-year-old was found guilty of adopting an aggressive attitude towards counterpart Jim Duffy and match officials at the 0-0 draw on 29 March.
Lennon's ban begins immediately, with a further two games suspended should he offend again in 2017.
Hibs were fined £750 for player behaviour at the final whistle.
The Edinburgh club, who have won the Scottish Championship title and promotion, will have to pay a further £250 should they transgress again before the end of the year.
Lennon will watch games against Raith Rovers and Ayr United from the stands but can return for the final day of the season at home to St Mirren when Hibs are presented with the league trophy.
A Scottish FA tribunal upheld a complaint that "on or around the 93rd minute, three or more players and/or members of team staff from your club were involved in a confrontation with opposing players and/or members of team staff".
Lennon was accused of adopting "an aggressive attitude to... Jim Duffy and/or a player from Greenock Morton FC".
He was also charged with "immediately following on from the dismissal of Darren McGregor of Hibernian FC, you did adopt an aggressive attitude to the match officials".
However, a charge that he had also adopted an aggressive attitude towards Morton striker Kudus Oyenuga was "not proved".
Tempers flared after Oyenuga was dismissed for a foul on Hibs defender Jordon Forster in front of the home dugout.
Hibs' Darren McGregor was also red carded for confronting Oyenuga, but that was later reduced to a booking after an appeal against referee Nick Walsh's decision.
Duffy has already been served with a two-match ban, with another game suspended should he transgress further.
Morton were fined £500, with £250 suspended.
Hibernian head coach Neil Lennon has been given a two-game touchline ban and his club fined after their stormy game against Morton.