The letter has been signed by 52 of the 90 MLAs. They represent Sinn Fein, the SDLP and the Alliance Party.
Sinn Fein Stormont leader Michelle O’Neill is among the signatories.
In a tweet she described the “unilateral actions of Boris Johnson” as “utterly reckless”.
“It is clearly a breach of International Law. The impact on our businesses & economy could be colossal. The pro-protocol parties have jointly written to Boris Johnson today to firmly reject his legislation and approach,” she tweeted.
Irish Foreign Affairs Minister Simon Coveney has also stated his opposition to the proposed legislation, saying it would “ratchet up” tension and breach the UK’s international commitments.
However Mr Johnson has said the plan to effectively override parts of the Brexit deal with Brussels was “not a big deal”, and would introduce “relatively simple” bureaucratic changes.
The letter to Mr Johnson from the 52 MLAs said they “reject in the strongest possible terms your Government’s reckless new Protocol legislation, which flies in the face of the expressed wishes of not just most businesses, but most people in Northern Ireland”.
It continues that “Whilst not ideal, the protocol currently represents the only available protections for Northern Ireland from the worst impacts of that hard Brexit”.
The MLAs say they share the desire to see post-Brexit arrangements work as smoothly as possible, but said the best way to achieve this is through engagement with the European Union.
“It is clear that solutions are available and deliverable – as have already been delivered in the area of medicines – but this must be on the basis of trust and the rule of law rather than law breaking and unilateral abrogation of treaty obligations,” they say.
The MLAs said they “strongly reject” Mr Johnson’s claim to be protecting the Good Friday Agreement.
“To complain the Protocol lacks cross-community consent, while ignoring the fact that Brexit itself – let alone hard Brexit – lacks even basic majority consent here, is a grotesque act of political distortion,” they write.
“Your claims to be acting to protect our institutions is as much a fabrication as the Brexit campaign claims you made in 2016.”
They concluded: “We will resolutely oppose this reckless Bill and continue to promote post-Brexit solutions on the basis of trust and honesty.”
Commenting on the letter signed by 52 of Stormont’s 90 MLAs objecting to the Government’s legislation, DUP leader Sir Jeffrey Donaldson said: “I want to be clear that those parties do not represent unionism.
“They represent one side of this debate and this institution in the Assembly can only be restored on the basis of a cross-community consensus, majority rule will not cut it.
“That’s what unionists were told over all the years. You cannot in a divided society operate on the basis of majority rule.
“So, to the Alliance, the SDLP and Sinn Fein who have written this letter, they need to recognise that these institutions can only function with the consent and support of unionists.
“Not a single (unionist) assembly member elected here at Stormont supports the protocol and that issue needs to be dealt with and, in the absence of an agreement with the EU, then the UK Government is right to act and we look forward to giving full consideration to this legislation.”