Labour's critics say she was "too able"
The First Minister, Jack McConnell, has accepted her resignation but in a letter to Ms Alexander expressed his regret at her departure.
Ms Alexander, 38, had considered standing for the first minister's post after the resignation of Henry McLeish last November, but stood aside when Mr McConnell ran for the office.
Mr McConnell is now under fire from political opponents for packing the Cabinet with "cronies".
BBC Scotland's political editor Brian Taylor said she had become "increasingly discontented with her workload and relations with colleagues".
He added: "This is a substantial blow to Jack McConnell's attempts to preserve the unity of his Labour group.
"Wendy Alexander's resignation is thought to be linked to personal disaffection with her role in Cabinet."
But a Scottish Executive spokesman denied that she had resigned after being overburdened in last autumn's cabinet reshuffle.
Dynamic force
This saw her take on the additional responsibility of transport in addition to enterprise and lifelong learning.
He also rejected suggestions that she was resigning out of pique, or for personal reasons.
"She gave Mr McConnell the letter, which intimated that she felt the time had come for her to stand down as a minister," he said.
"She has been thinking about this since the turn of the year, but she wanted to finish the task of preparing a new transport strategy."
Friends said Ms Alexander, regarded who has been regarded as a dynamic force in the Labour Party, she wanted to concentrate on where her real interests lay - the formulation of policy.
Deputy Enterprise Minister Lewis Macdonald will stand in for her for the time being until a successor is chosen by Mr McConnell.
'Deeply unhappy'
Amongst the reaction from political opponents, Scottish Tory leader David McLetchie declared: "It has been obvious for some time that Wendy Alexander has been deeply unhappy, ever since the election of Jack McConnell as first minister.
"Today marks the final parting of the ways.
"We now have a Cabinet entirely packed with Jack's cronies and Wendy Alexander now joins the Cabinet-in-exile on Labour's backbenches."
Scottish National Party leader John Swinney said Mr McConnell had tried to "work her into the ground" by heaping responsibilities on her.
"The tragedy of this is that Scotland will now be governed by a Cabinet of cronies," he said.
"It seems talent is now seen as a handicap to Labour ministers and a threat to Jack McConnell."
In March last year, she was the subject of a complaint about "interference" by the chief press officer in the enterprise department.
Scotland's senior civil servant decided against carrying out a formal inquiry.
'Strong enthusiasm'
Her work within the Scottish Executive will be best remembered for steering through the repeal of the legislation known as Section 28, which lifted the ban on the promotion of homosexuality by local authorities.
In her resignation letter to Mr McConnell, she wrote: "My enthusiasm for the parliament remains as strong as it was, over 20 years ago, when we campaigned together for its creation.
"It is an honour to represent the people of Paisley North and I hope to win their support again at the election in 2003."
Mr McConnell wrote back that he understood the pressures of political life and the "demands it makes on all of us".
He added: "Whilst I regret your decision to resign I understand too, your wish to take a well deserved break from those pressures and I accept your resignation."
She was first appointed five years ago this weekend to work as an adviser for the late First Minister Donald Dewar.
The high-flying politician, who holds an MBA and was a business consultant before entering politics full-time, whose brother Douglas is MP for Paisley South, spent three years in the Scottish Cabinet.
She is out of the country at present.