Those most likely to be affected include older couples in parts of Edinburgh and the Lothians who have seen their property values soar in recent years but are not cash rich.
Scottish Labour said that the tax would raise £3.7 billion and target the richest 10 per cent of the population, with a 1 per cent levy on their savings and pensions as well as assets such as property.
This could hit households with a combined “wealth” of £1 million.
But Scottish Government figures reveal that this would disproportionately hit pensioner households.
The breakdown of the top 10 per cent of the wealthiest Scots shows pensioner couples (31 per cent) make up the lion’s share of this, according to Wealth and Assets in Scotland 2006-14. In addition, 12 per cent are a couple with one is a pensioner and 6 per cent are single pensioners.
SNP MSP Bruce Crawford said: “For pensioners, being asset-rich does not necessarily mean having a high income.
“It’s not entirely clear how they would afford to pay, unless Richard Leonard expects them to sell their homes to pay a one-off tax bill.
“In fact, Labour oppose giving the Scottish Parliament the full powers over tax and welfare that would give us the flexibility to deal with inequality in a much more effective way.”
The Scottish Government report defines wealth as house value, savings, financial assets, including stock and shares, as well as pensions value.
It also includes the value of physical assets such as cars and domestic appliances.
Mr Leonard says Holyrood could introduce the wealth tax using an “order in council” in the original Scotland Act.
“A Labour spokesman said: “With foodbanks, homelessness and child poverty continuing to hold a grip on too many lives, this intervention from the SNP seems ill judged.
“Many SNP voters will be surprised that the party would choose to attack Labour for considering radical solutions to inequality in Scotland.”