Also the API has not. But you can use the time in millisecond for your selection:
Blocks for one day: https://blockchain.info/de/blocks/$time_in_milliseconds?format=json
See: https://blockchain.info/de/api/blockchain_api

But i am not sure, if this really helps. The other way round would be much more comfortable: Select with a hash and get the time in ms.

Is there any API? I didn't found.