The Educational Institute of Scotland (EIS) said internal assessments would normally have been finished by the end of term, leaving time over Easter to revise for exams.
However, Larry Flanagan, the union's general secretary, said delays had been caused by the difficulties schools have had implementing new National 4 and National 5 qualification, which replace Standard Grade.
The internal assessments, which are marked by teachers and verified by the Scottish Qualifications Authority (SQA), are vital because National 4 qualifications have no external exam.
Internal assessments are also an integral part of the National 5 qualifications, although pupils will sit exams over the next few weeks.
Mr Flanagan said: "We are hearing anecdotally that schools are having to bring pupils in over the Easter holidays to finish internal assessments.
"It is symptomatic of the difficulties schools have had dealing with the excessive workload associated with the new exams and the fact the amount of internal assessment has been disproportionate."
Mr Flanagan called on the Scottish Government to hold a review of the im plementation of the National qualifications to learn lessons for the future.
He added: "It is important everyone associated with the introduction of the National qualifications reflects on what has happened.
"It was one of the intentions of the new system to reduce the burden of assessment on pupils, but that has not happened.
"We are also moving straight into the implementation of the new Higher exams and it is absolutely vital that goes well."
Alan McKenzie, acting general secretary of the Scottish Secondary Teachers Association, also said members had highlighted the extra classes for pupils.
He said: "We are aware of several councils who are using the Easter holidays to try and get these assessments finished and to catch up. There has been a difficulty getting everything done in time this year. It is because of the well-documented difficulties schools have been having implementing the new qualifications."
A spokesman for the SQA said: "We take our responsibility to uphold the high standards of Scottish qualifications very seriously and have put systems in place to ensure the assessment of the new qualifications is high-quality, rigorous and meets national standards.
"Change always throws up challenges, and we are very conscious that teachers need support to implement the new qualifications. That's why we have worked hard, alongside Education Scotland, to offer the support and materials needed to make the new qualifications a success. "
The new qualifications were introduced as part of the Curriculum for Excellence (CfE) reforms designed to provide a broader education for pupils. It was also the intention to move pupils away from "mindless" rote learning simply to pass exams, with a greater focus on project work.