SNP MP Stewart Hosie has said he will step down as the party's deputy leader in the autumn.
His announcement comes after newspapers reported he had been involved in an affair with journalist Serena Cowdy.
In a letter to party leader Nicola Sturgeon, he apologised for "any hurt and upset I have caused to friends, family and colleagues".
Ms Sturgeon praised his work for the party, adding he would continue to make a "valuable contribution".
Mr Hosie is expected to remain SNP Treasury spokesman at Westminster and deputy leader of Westminster group.
In his resignation letter, he said: "As you know I have been admitted to hospital on three occasions in the past few years with very high blood pressure.
"In that regard, the stress of the intense scrutiny of my private life has been very difficult."
Who is Stewart Hosie?
- Born in Dundee in 1963
- Worked in IT for 20 years and ran his own business
- Married to Shona Robison MSP for Dundee City East and Scottish Health Secretary. They have one daughter
- Elected MP for Dundee East in 2005, gaining his seat from Labour
- SNP spokesman at Westminster on the Treasury and deputy leader of the SNP Westminster Group
- Following the aftermath of the Scottish independence referendum in 2014 he was elected deputy leader of his party after Nicola Sturgeon stepped down from the post to stand for the leadership
The politician recently separated from his wife, SNP MSP and Scottish Health Secretary, Shona Robison.
He said it was "never his intention" to hurt or upset anyone.
He went on: "I am also writing to tell you of my intention not to seek re-election as deputy leader of the SNP at this year's annual conference, giving ample time for the party to choose a successor.
"I intend to concentrate on my constituents, my responsibilities at Westminster, and most importantly, my health."
BBC Scotland's Westminster correspondent Nick Eardley said SNP sources had told him there was no pressure for Mr Hosie to stand down and his decision was "personal".
"I'm told it was never confirmed that he would lead the party's summer independence campaign, but he'll now play a much less central role than he would have," he added.
The announcement comes a day before Ms Sturgeon is due to address MPs at Westminster.
Responding to Mr Hosie's letter, the SNP leader paid tribute to his work as deputy leader and in particular to his work on the 2015 and 2016 election manifestos.
She said: "As you step down as deputy leader, I know you will continue to make a valuable contribution to the party in many ways and, in particular, through your work in your constituency and as part of the Westminster group."
Earlier this week Scottish Conservative MSP Jackson Carlaw reported both Mr Hosie and another SNP MP, Angus MacNeil, to the Parliamentary Standards Commissioner over allegations they claimed expenses for accommodation while carrying out extra-marital affairs with Ms Cowdy.
'Source of embarrassment'
Ms Sturgeon told the BBC she had seen no evidence of any breach of parliamentary expenses rules.
The first minister was photographed in the Holyrood chamber embracing Ms Robison who has been married to Dundee East MP Mr Hosie for nearly 20 years.
Shadow Scottish secretary Ian Murray MP said: "Stewart Hosie has made the right decision to resign, but this incident exposes something more significant about the SNP at Westminster.
"Instead of attacking each other, SNP MPs should be focused on delivering for their constituents.
"Last year the SNP told us their MPs would be stronger for Scotland, but just 12 months on many have been a source of real embarrassment."
Scottish Conservative MSP John Lamont said: "This episode has been another embarrassment to the SNP MPs group and people who voted for them last year have every right to question what has happened since.
"In the meantime, questions still remain to be answered about the way public money has been spent, both by Mr Hosie and Angus MacNeil."