The plans went before the Scottish government for consideration that month.
They would have brought specialist services from across Lanarkshire – including cancer care, renal medicine, urology services and ear nose and throat surgery – under one roof.
They also suggested turning the current Monklands site into a “healthcare village”.
However, the Scottish government said the proposed design “would not deliver value for money for the public purse”.
In a statement, Constance said the £2.1bn outlay was “significantly more expensive than comparable programmes” and that it would “represent an unprecedented concentration of capital investment in a single health project”.
She said the total cost would amount to about £5m per bed.
Constance said: “I recognise this will be disappointing for staff and communities who have been engaging patiently for a number of years in the development of plans.
“This is not a decision I have taken lightly – we are fully committed to building a new hospital at Monklands.
“However, it is also my responsibility to ensure that major investment decisions are affordable, deliverable, and aligned with the future direction of our health and care system.”
A spokesperson for North Lanarkshire Council said it had invested significant resources into the project and that the local authority was surprised by the announcement.
She said: “This announcement has come as a surprise as we have been working extensively with NHS Lanarkshire over the last decade on the Monklands Replacement Project and invested significant resource in the planning and infrastructure elements, which would have seen a long overdue state-of-the-art acute hospital for Lanarkshire.
“We are urgently seeking clarity about what the redesign will actually mean for modern, accessible healthcare for the people of North Lanarkshire and for the existing workforce whose hopes for a new replacement hospital were firmly aligned to improved quality of care for their patients.”