Sandy Cooper was one of three people chosen to represent the Elgin City North ward in last week's election.
He tendered his resignation in a letter to the council's chief executive. When contacted by BBC Scotland and asked about his decision, Mr Cooper said: "It's just not for me."
The by-election will be held on 13 July, with the count the following day.
Moray Council said Mr Cooper's nomination papers contained no party or political affiliation.

Only three of the Brazilian club's players survived November's crash, when 71 of 77 people on board died.
Top clubs from Brazil and Argentina offered to loan players to Chapocense, who signed 25 new players this season and promoted nine from the youth team.
They lifted the Santa Catarina state championship on Sunday for the second straight year, despite losing to Avai.
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Chapecoense were beaten 1-0 in Sunday's final play-off, but their 1-0 victory in the first leg meant their better record over the course of the season was decisive.
The club dedicated the win to those who were killed, with new coach Vagner Mancini saying: "We knew that Chape would have a lot of difficulties because of the rebuilding of the team, but because of the work we reached the title, beating opponents who are rivals and difficult to beat."
The crash happened on 29 November as the squad travelled to face Colombian side Atletico Nacional in the final of the Copa Sudamericana. Nineteen players and staff died.

His election ends a period of uncertainty as he replaces Chabur Goc Alei, who was suspended by the SSFA's general assembly last year.
Amin beat former international referee Lual Maluk Lual in the polls which were overseen by delegates from Fifa and the Confederation of African Football.
"Let's forget our differences but be united by the beautiful game of football," Amin said.
"I welcome all my opponents to come and join hands so that we develop football in our beloved country South Sudan."
Alei was forced out of office amid allegations of mismanagement.
Amin is a well-known businessman in Juba and is a former board member with local club Atlabara.
Venasio Deng Amun will be Amin's deputy after he beat Sestilio Juba Leriba in the polls for vice-president.

No batsman from Bapchild Cricket Club was able to get off the mark against Christ Church University in Canterbury.
"We couldn't believe it, all they needed to do was hit a wall to get one run," Christ Church player Mike Rose told the Crawley Observer.
Somerset club Langport set the record for the lowest score when they were dismissed for zero in 1913.
Wirral CC were bowled out for three in a Cheshire League Division Three fixture in 2014 - though they had 11 players and were 0-8 at one stage.
And Kent village team Saltwood CC scored 216 before bowling Martin Walters out for zero in 8.2 overs during a match in 1964.
In first-class cricket, the lowest score ever made is six - by "The B's" against England at the old Lord's ground in 1810 - while New Zealand's 26 against England in 1955 remains the lowest total scored in a Test match.

Read the team news for Saturday's matches below.
Kick-off 15:00 unless stated. All times GMT.
Manchester City v Chelsea (12:30)
Crystal Palace v Southampton
Stoke City v Burnley
Sunderland v Leicester City
Tottenham Hotspur v Swansea City
West Bromwich Albion v Watford
West Ham United v Arsenal (17:30)
Birmingham City v Barnsley
Blackburn Rovers v Huddersfield Town
Bristol City v Ipswich Town
Burton Albion v Rotherham United
Cardiff City v Brighton and Hove Albion
Fulham v Reading
Norwich City v Brentford
Sheffield Wednesday v Preston North End
Wigan Athletic v Derby County
Leeds United v Aston Villa (17:30)
A date for a by-election after a new councillor resigned only days after being elected in Moray has been set.
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Chapecoense have won their first title since most of their team were killed in a plane crash.
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Francis Amin Michael Paul has been elected as the new president of the South Sudan Football Association (SSFA).
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A cricket team was bowled out for 0 in just 20 balls in a county six-a-side indoor championships match.
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Four of the Premier League's top five are in action on Saturday, while there is a packed programme in the Championship.