The state pension age is set to go up from 65 to 66 by 2020 and eventually up to 68, and Lord Hutton has called for public sector pensions to match it.
Mr Burnham has asked for the plans for teachers to be reviewed, arguing that the "high levels of energy, commitment, concentration and stamina" the job requires mean some will be unable to keep going longer.
He called for changes to be delayed so a study on the effect of altering retirement age on the standards of teaching in other countries can be carried out.
In a letter to education secretary Michael Gove he wrote: "Teaching is an extremely demanding profession, requiring high levels of energy, commitment, concentration and stamina.
"We have excellent teachers of all ages in our schools, but some feel that they can no longer meet the demands of the classroom after the age of 65.
"Of course, increasing longevity means we need to look at changes to the retirement age, but exemptions have already been made for police officers and firefighters. We need to understand the implications of expecting teachers to work until they are 68, not only for teachers but for the school system as a whole."
Mr Burnham reiterated the unions' calls for a full valuation of the Teachers' Pension Scheme (TPS) and said that the start of talks with the education unions specifically on the TPS gave the Government the opportunity "to take the heat out of this situation".
The letter comes after the Department for Education last week announced a consultation on plans for the first wave of increase in teachers' pension contributions in 201213. The first phase would account for around 40 per cent of the total rises and would see teachers earning pound;32,000-pound;40,000 a year paying 19 per cent more towards their pensions.
NUT general secretary Christine Blower said that beginning the consultation during the political recess - "when there will be little chance for scrutiny" - was a "cynical move".
Schools minister Nick Gibb said the proposed increases for 201213 were approximately the same as those put forward in Labour's pre-budget report in 2009, which were agreed with the unions in 2007.