The 44-year-old joined the club in November 2011 after leaving his previous role at Irish outfit Bohemians.
Hibernian have started the campaign in inconsistent fashion, amassing 15 points from 11 fixtures.
The Edinburgh outfit were hoping to build on last year's seventh-place finish, where the team won and lost 13 of their top-flight fixtures.
But their early-season form has failed to show Hibs can contend in the upper echelons of the table.
Hibs' misery was compounded with a 1-0 loss at home to rivals Hearts in the Scottish League Cup on Wednesday, courtesy of Ryan Stevenson's first-half strike.
And that has led to Fenlon - who has also had spells at Shelbourne and Derry City - leaving his post at Easter Road.
He said: "It is a difficult decision for me, but it is the right decision.
"Jimmy (Nicholl) will take the team on Sunday.
"I've been privileged to manage this fantastic football club and I really hopes it does kick on now."
Hibernian will look to improve their league fortunes in Saturday's visit to Motherwell.
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