Duffy, 57, was charged with misconduct for entering the Hibs technical area at Easter Road on 29 March and adopting an aggressive attitude towards Lennon.
The same complaint against assistant Craig McPherson was withdrawn.
Duffy faces an additional one-game ban if he transgresses again in 2017, while Morton were fined £500 for the stoppage-time fracas.
The Greenock club will need to pay another £250 in the event of a further breach of disciplinary rule 204, with the charge stating, "three or more players and/or members of staff" were "involved in a confrontation with opposing players and/or staff".
Lennon postponed his hearing due to the non-availability of Hibernian's solicitor. His case will be heard on 25 April.
The Hibs boss faces three charges of "adopting an aggressive attitude" to Morton striker Kudus Oyenuga, Duffy and the match officials.
Tempers flared during the Championship 0-0 draw after Oyenuga was dismissed for a foul on Hibs defender Jordon Forster right in front of the home dugout.
Hibs' Darren McGregor was also red carded for confronting Oyenuga, who fell to the ground, but that was later reduced to a booking after an appeal against referee Nick Walsh's decision.
Morton manager Jim Duffy will serve a two-match ban following his touchline altercation with Hibs boss Neil Lennon.