In a statement on Saturday night, Fisher, the head of policy, will leave his post by the end of the year "to spend more time with his young family", the BBC reported.
Fisher said he feels "immensely proud about what we have collectively achieved".
But he added that "the long hours, stresses and strains that inevitably come from working in this high pressure environment mean I haven't managed to balance my commitments to my wife and young son".
"So after four years, I'm now choosing to prioritise them. I will stay on for any autumn general election, but will be leaving by the end of the year."
Fisher is said to have revealed his intention to quit on September 14, according to a memo seen by the Sunday Times.
The newspaper reports that he criticised Corbyn's team for their "blizzard of lies".
Fisher's decision to quit emerged just hours after Corbyn quashed a motion at his party conference on Saturday to oust Labour's deputy leader Tom Watson Watson, by abolishing his position.
An initial attempt had been made at the Labour National Executive Committee (NEC) on Friday.
Corbyn later suggested the role should be reviewed instead, and his suggestion was backed by the ruling NEC, the BBC said.
He has since told the Sunday Mirror he would like to see the party have two deputy leaders "which reflects diversity within our society".
Corbyn told the newspaper one deputy leader would be a woman.
"Tom is the elected deputy leader of the party and so has an important role to play. I work with him and he's done very well on media reform, online gambling and exposing the way sugar has a deleterious affect on our lives."
( With inputs from IANS )