The bond note, which is worth one US dollar - the country's main currency since 2009 - is raising fears of a return to the ill-fated local dollar.
The move, first announced in May, has fuelled some of the biggest protests in a decade against President Mugabe.
The government has issued the bond note to tackle a worsening cash shortage.
It hopes the cash substitute, which is legal tender in Zimbabwe but is not valid outside the country, will halt the flow of US dollars going overseas.
Initially, an amount worth $10m is being introduced into circulation in two and five dollar denominations.
Business groups have welcomed the move as a way of boosting economic growth.
However, major opposition parties, workers and civil society groups are planning further protests this week.
And in the run-up to the notes' release, Zimbabweans queued for hours to withdraw their US dollars amid fears the bond notes would not be able to keep parity.
Zimbabwe's central bank has assured people the notes' release will be controlled, including weekly withdrawal limits of $150 worth.
Under a proposed law, anyone found guilty of defacing the notes could face up to seven years in prison.
They will become one of nine currencies accepted as legal tender in the country.
Zimbabwe's 2008-9 hyperinflation crisis in numbers
An egg cost 50 billion Zimbabwean dollars in 2008
A loaf of bread cost the same as 12 brand new cars would have cost ten years previously
Inflation rates reached 231,000,000%
To keep up with the rising prices, a 100 trillion dollar note was issued - enough for a weekly bus ticket - before the Zimbabwean dollar was scrapped in 2009
Analysis: Matthew Davies, Editor of BBC Africa Business Report
The Reserve Bank of Zimbabwe has always steered clear of referring to the new bond notes as currency.
For ordinary Zimbabweans, memories of the collapse and demise of the Zimbabwean dollar in 2009, and the hyperinflation that caused its destruction, still rankle.
So, it's a question of "when is a currency not a currency?"
Withdraw from a bank today in Zimbabwe and you'll be issued with bond notes, which are officially interchangeable with the US dollar at a rate of one to one.
You can take the notes to the shops and exchange them for goods. All very well and good, you'd think.
But what a currency needs is confidence, and on the streets of Harare there seems to be precious little of that.
There were few alternatives for the Reserve Bank - the economy is experiencing a chronic shortage of US dollars, which have been the main currency of use for the past seven years.
But such is the fear that the bond notes will be unable to hold their parity with the dollar that their introduction has sparked the largest anti-government protests in years.
If the current experiment with bond notes even looks like taking a step backward to the hyperinflation of seven years ago, not only will the economy's very survival be in jeopardy, so too will the government's.