Uefa's control, ethics and disciplinary body imposed the punishment for "acts of violence against the referee".
Lennon was sent to the stand during last month's Europa League qualifying match against Brondby after remonstrating with officials.
He was automatically banned from the touchline for the return leg in Denmark, with Hibs losing on penalties.
The 45-year-old described his dismissal on his debut at Easter Road on 14 July as "pathetic".
The former Celtic boss was incensed after Jason Cummings had a goal disallowed after 30 minutes that television replays showed was onside.
Hibs lost the first leg 1-0 but levelled the tie away from home before Brondby won through on spot-kicks.
The Edinburgh club responded via Twitter, saying: "Hibernian are aware of the sanction imposed by Uefa on head coach Neil Lennon and are in the process of appealing the suspension."
Hibernian are to appeal against the five-match European ban given to manager Neil Lennon.