Critics said the proposals would allow the Scottish Government to "shut down schools and confine people to their homes at the drop of a hat".
The Coronavirus (Recovery and Reform) (Scotland) Bill would give ministers the ability to respond to public health emergencies in a similar way to legislation passed in the wake of Covid.
This includes imposing lockdown restrictions, allowing court hearings to take place remotely and restricting access to schools.
A consultation last year saw almost 3,000 responses from organisations and individuals, and MSPs will now scrutinise and debate the Bill.
The Scottish Government said the legislation would maintain provisions that enable ministers “to enact measures via public health regulations for any future public health threats, bringing Scotland into line with England and Wales”.
But Scottish Labour deputy leader Jackie Baillie condemned it as a “power grab”.
She said: “These emergency powers were a necessary response to an unprecedented crisis, not a free pass for ministers to hoard new powers.
“This Bill would give ministers permanent powers to shut down schools and confine people to their homes at the drop of a hat.
“There is simply no excuse for bypassing Parliament, when Holyrood has shown time and time again that it can respond with the urgency needed.”
Scottish Conservative Covid recovery spokesman Murdo Fraser said: “Whilst there may be measures in this Bill that are sensible long-term reforms, too much of it amounts to an unwarranted and unacceptable power grab by the SNP.
“The powers it would hand the Scottish Government permanently were only ever meant to be temporary for the duration of the pandemic.
“The most worrying of the proposals is the power to close schools and to release prisoners early – and the proposed Bill lets them do this without prior Parliamentary approval.
“This Bill is an alarming and unnecessary overreach by the SNP, so the Scottish Conservatives will oppose measures which put too much power in the hands of ministers.”
Deputy First Minister John Swinney said the Scottish Government has "already removed many of the temporary measures that supported our response to the pandemic, which are no longer needed".
He said: “However, we believe those pragmatic reforms that have delivered demonstrable benefit to the people of Scotland should continue.
"Whilst it has been incredibly disruptive, the urgency of the pandemic has driven the pace of digital adoption, and in some cases more efficient ways of working, and better service to the public.
“I am grateful to everyone who took the time to respond to our consultation, which has been considered very carefully in the drafting of this Bill, to embed these beneficial reforms in Scotland’s public services, along with the temporary extension of some justice measures to assist the courts with clearing the backlog of cases arising from the pandemic.
“Our priorities are to continue to lead Scotland safely through and out of the Covid pandemic, to address inequalities made worse by Covid, make progress towards a wellbeing economy and accelerate inclusive, person-centred public services, and this Bill supports those aims.”
The new Bill proposes changes in 30 legislative areas, which were modified by temporary provisions made under Scottish and UK coronavirus legislation.