Andrew Travers left the authority by "mutual agreement" after the error, officials said.
Voters were initially turned away from all 155 polling stations in the borough because their names were missing from the poll list.
An independent investigation has been launched, the council said.
In a statement issued through the council, Mr Travers said: "I have enjoyed my time at Barnet and I believe the changes we have put in place and the continued programme of growth and transformation will enable the borough to continue to thrive."
A council spokesperson said Mr Travers had "made a valuable contribution to the council during his three and half years as chief executive."
Deputy chief executive John Hooton will take over temporarily while longer term arrangements are put in place, the council said.
On election day, staff at one station said just three of the first 30 voters to show up were on the register. The rest were told to come back later.
Barnet Council apologised for the problems and later offered emergency proxy votes to residents who had been affected.
But voters in the area questioned how the result could be "fair" when not everyone was able to have their say at the ballot box.
A statement released by Mr Travers on Thursday blamed electoral registration lists for the problems.
The council's review will conclude by the end of May and the findings will be presented publicly to the General Functions Committee.
It will look at the "appropriateness" of arrangements in place for the EU Referendum in June.
A spokesman said it was currently in discussions to establish who would lead the investigation.
The chief executive of Barnet Council has left his role after a blunder led to some voters being turned away from polling stations on Thursday.