The delay means staff will not have enough time to prepare lesson plans to teach the new qualifications in August, the Scottish Secondary Teachers Association (SSTA) has said.
Although schools have been given permission by the government to delay them for a year, the SSTA said some councils are pressing ahead regardless.
The warning comes in a written submission by the teaching union to the Scottish Parliament's education committee, which is looking at the roll-out of new school exams.
The new Highers are part of wider reforms, which have also seen Standard Grades replaced by National exams.
They have been updated to make material more relevant and also to fit in with the aims of the new Curriculum for Excellence (CfE), which seeks to teach pupils a broader range of skills.
Schools struggling to introduce the National qualifications argue the introduction of a new Higher places too great a burden on staff.
The SSTA submission states: "The insistence of some local authorities that the new Highers will go ahead next year, regardless of the professional judgement of teachers ... is particularly problematic in some subject areas.Many members feel that with only months until new timetables start, not all the new Higher courses are available. Where is the time to prepare new courses in time for this?"
The SSTA said the resulting pressure on teachers had led to significant increases in workload.
"This is an enormous issue. Many respondents report working in excess of 50 hours a week, some many more hours than that. Many teachers report high levels of stress, absence, or sleeplessness because of anxiety and uncertainly," it said.
A submission from the Educational Institute of Scotland (EIS) teaching union also raised concerns about the new qualifications, arguing the founding aims of CfE were no longer being observed.
The work of the Scottish Qualifications Authority (SQA), the national quango responsible for the new qualifications, came in for particular critcism. The EIS submission states: "It is clear that the current implementation ..... is far removed from the envisaged aims of maintaining breadth, reducing the burden of assessment and creating additional time for teaching and learning with the aim of promoting deeper learning.
"It would not be an exaggeration to say that we have not encountered as widespread anger and disappointment and frustration with the exams authority as we are currently witnessing."