First floated in January and included in the Conservative manifesto, the cap would apply to central and local government and other public bodies.
The BBC, Channel 4, Bank of England, the Armed Forces, Royal Bank of Scotland and other taxpayer-owned banks would be among organisations exempt.
But ministers said they would expect such bodies to introduce "their own, commensurate cap on exit payments".
The government says it wants to significantly reduce the cost to the taxpayer of public sector pay-offs, which totalled about £6.5bn between 2011-12 and 2013-14.
"It's not right that highly-paid public sector workers should receive huge taxpayer-funded payouts when they're made redundant," said Chief Secretary to the Treasury Greg Hands.
"The cap we are bringing into law will mean no more six-figure pay-offs in the civil service, local authorities and the NHS. We also expect other bodies who rely on taxpayers' money to follow suit."
Under its plans, which would apply to bodies whose remuneration is determined at a UK level, any eligible organisation which wanted to exceed the cap would have to seek permission from ministers.
The Treasury-led consultation, which will seek views on the scope, level and design of the proposed cap, will close on 27 August.
Union leaders criticised the exclusion of RBS and the firms which manage the remaining publicly owned assets of Northern Rock and Bradford and Bingley.
They claim the cap will potentially affect nurses, teachers, firefighters and police officers on relatively modest incomes.
"Ministers are portraying this as being aimed at highly paid public servants who enjoy 'golden goodbyes'," said Mark Serwotka, from the Public and Commercial Services Union.
"But the reality is that capping the redundancy payments at the proposed level will impact on long-serving, loyal staff earning just above the average civil service pay who have built up pensions and other entitlements under their terms and conditions."
The BBC introduced a £150,000 maximum limit on redundancy payments in 2013 following criticism of severance packages paid to some departing senior executives.

Like-for-like cycle sales fell 4% in the three months to 1 July, which chief executive Jill McDonald blamed on poor weather and the timing of Easter.
Halfords hopes that new bike ranges designed with Sir Bradley Wiggins and Laura Trott, who are both competing in the Rio Olympics, will boost demand.
In the year to March, bike sales at Halfords had fallen by 0.9%.
Halfords said that sales of premium bikes, which are priced between Â£500 and Â£5,000 and include the Pinarello model ridden by Team Sky, performed well over the first quarter. However, wet weather and the timing of Easter affected sales of mainstream models and accessories.
Overall, Halford's like-for-like sales fell 0.6%. Its retail division gained from strong demand in car maintenance and for child safety seats, but declining sales of sat navs dragged revenues at its car enhancement sector down 4.2%.
Halfords said in June that it expected the weak pound to knock Â£3m off its profits. Following the steep fall in sterling against the dollar since Britain voted to leave the European Union, the company said it may have further small impact in the financial year.
Commenting on Brexit, Ms McDonald said: "While the recent decision to leave the EU does create uncertainty, we are well-positioned as a business and focused on delivering sustainable long-term growth."
Ministers are to consult on plans to cap public sector pay-offs at £95,000.
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Halfords is hoping for an Olympics bounce to stem a slide in bike sales, which have continued to fall.