The city council is currently advertising a total of 31 vacant teaching posts, involving a range of subjects and including one for a headteacher.
Lothian Conservative MSP Miles Briggs said the number of teaching vacancies meant other teachers were having to cover extra classes on top of the ones they had already and claimed there would be a knock-on effect on pupils.
He said the teacher shortage came at a time when Education Secretary John Swinney had warned that Scotland was facing “a very challenging period in education”.
But council chiefs played down the number of vacancies and said when previous posts were advertised there had been a good response.
Earlier this month, Mr Swinney insisted there was no crisis in morale among Scottish teachers despite complaints about punishing workloads and low pay.
He said: “I don’t think we have a crisis in morale. I think what we have got is a very challenging period in education where we have some staff shortages.
Mr Swinney said the last survey of vacancies suggested Scotland as a whole was about 800 teachers short across the country.
Mr Briggs said the Capital’s vacancies should have been tackled before the schools returned on 14 August after the summer holidays.
He said: “Edinburgh parents that I have spoken to would really have liked more to have been done to fill these positions before the start of term to minimise any disruption to classes.
“Hard working teachers are being asked to cover even more classes because SNP have proven again that they are not capable of managing workforces effectively.
“This will unfortunately have a knock-on effect for pupils because of disruptions within schools and teachers being spread more thinly.”
City education convener Councillor Ian Perry said: “We don’t have a major issue in Edinburgh with teacher recruitment, as shown earlier this year when our recruitment campaign for 34 posts attracted over 557 applications.
“We currently have 31 vacancies advertised out of a total of 3,500 teacher positions which is less than 1 per cent of the total number of teachers.”