Laurence Gough, 66, who had most recently been running the Eskimo Joe’s frozen food stall, started working at the market in 1976.
But, now suffering from leukaemia, Mr Gough can no longer continue running the stall, for which traders pay a rent fee to Leeds City Council.
He had agreed with the council to close at the end of October.
But as his illnesses have progressed, he has become too poorly to continue working and is now in hospital.
The stall closed for business on Saturday.
Now his son, and fellow stallholder, Neil Gough, has claimed the council has “no compassion”, after telling his dad that he will still have to pay around £1,000-a-week rent despite being too ill to work, until the termination period has elapsed.
Mr Gough, 45, told the YEP: “For 42 years he has been down here and my dad has always paid his rent on time and never missed one.
“We asked the council for a bit of compassion because my dad isn’t well enough to keep working. They just said ‘no’. “I just thought it was very cold.”
A council spokesman told the YEP it was open to meeting Mr Gough to discuss the issue more.
Laurence Gough started working at his first stall in Kirkgate Market - M & G Fruits - in Leeds city centre more than 40 years ago, when he was just 21-years-old.
His son, who runs Neil’s Quality Greengrocer, said: “He’s very well-liked in the market, everyone knows him.
“My dad is an old school market trader: comes in does his graft and goes home.”
A council spokesman said: “Leeds City Council has been in dialogue with Mr Gough over this issue.
“We are understanding and fully supportive of his current situation, and remain open to meeting him again to discuss the position further.”