Personal Independence Payments (PIP) were originally due to replace Disability Living Allowance (DLA) from the beginning of October, before the date was put back to tomorrow.
But, rather than across Britain, the Government will roll out the benefit only for claimants in certain areas. The adjustment to the timetable will affect Scotland.
A spokeswoman for the support and campaigning group, Capability Scotland, said: "It is important that the UK Government takes time to get the assessment process right. However, this delay may cause additional uncertainty for the huge numbers of disabled people already concerned about the introduction of Personal Independence Payments."
Labour's shadow work and pensions secretary Rachel Reeves said it showed there was chaos in the department.
She said: "The delivery problems we are seeing at the Department for Work and Pensions now risk descending into farce. But for thousands of disabled people who are already extremely anxious about the changes, this is no joke."
Dame Anne Begg, Labour MP for Aberdeen South and chair of the Work and Pensions Select Committee, said delay in itself was not a bad thing, but warned it would cause claimants anxiety.
There are around 3.3 million DLA claimants, aged 16 to 64, who will be moved to PIP over the next few years. The benefit - worth between £21 and £134.40 a week - is available to disabled people who have difficulty walking or need help to look after themselves.
Under the PIP system, which introduces regular written and face-to-face medical assessments, claimants will receive a daily living component of either £53 or £79.15 and a mobility component of either £21 or £55.25.
In a statement, Minister for Disabled People Mike Penning said: "DLA is an outdated benefit introduced over 20 years ago, whereas the new benefit is designed to better reflect today's understanding of disability, particularly with regards to mental health and fluctuating conditions."
Since June this year, all new disabled claimants have had to apply for PIP, and all current claimants whose circumstances have changed had been due to start moving to the new benefit tomorrow.
The change to the reform timetable means only those in Wales, the East and West Midlands and East Anglia will transfer to PIP from tomorrow if their condition changes.
The government said the need for the change had only came to light at the beginning of October.
A spokesman for the Department for Work and Pensions said ministers had deliberately chosen a phased introduction for PIP claim reassessments so the system could be regularly reviewed.