He said while it was important to preserve the architectural beauty of some of the churches, many of which have listed status, they may serve the community better by becoming secular.
His comments follow his suggestion earlier this month that libraries could benefit from being modernised with coffee bars and abolishing the silence rule, Telegraph newspaper reported.
Burnham said if the UK could not preserve its churches: "We need to find new purposes with the support of the local community and we need to increase secular interest in our church heritage."
He used the example of the recent multi-million pound renovation of All Souls Church in Bolton, an Anglican church which has "found a new multi-faith, multi-racial community to serve."
He added: "My department worked with The Churches Conservation Trust (CCT) to save All Souls.
"The CCT came up with a brilliant solution. The community did not need a museum piece but they did need somewhere to meet. They needed a gym, a health centre, space for community education and space for inter-faith learning."
He also used an example of a former church, St Peter's in Liverpool, which had been turned into a themed restaurant and bar called Alma De Cuba in 2005.
"My mum said the last time she set foot in the building was 40 years ago for confession," he said, adding "Not everyone will be happy with that transformation. Part of me was uneasy but to her credit, my mum, a good Scouse Catholic, shrugged and raised a glass."
While the more pious did sound outraged at the minister's suggestion, others seemed to shrug it away. The church's own reaction seemed low-key.
A Church of England spokesman said Burnham's suggestion would only apply to a minority of its 10,000 churches now deemed redundant - about 30 a year.