Practically speaking, I think that - in the realm of cryptography - a HSM is the closest that you can get. A HSM is a tamper-proof box that destructs or disables the keys and data stored within it when it detects distortion.
Of course a HSM is a practical device; it doesn't provide information theoretic certainty that the information will be destroyed. Although it operates as a black box, it is still a physical device and there are certainly attack vectors on it. Internally it is just a computer in a tamper resistant box. These expensive devices are protected against many kinds of side channel attack. They also try and resist transport, by detecting movement and by destroying all data if the power is removed from them (they commonly include a battery / ultra capacitor to store power to do so, or they rely on volatile RAM in the first place. There are cheaper / more limited devices that simply rely on a smart card chip to perform the same functionality; these often are in the form of a largish USB-stick.
One trick you can perform once you have a secure key store that provides cryptographic operations on the keys is to encrypt data with such a key. You could put a limit on the key usage, say 2 - once for writing, once for reading - for symmetric keys, or just 1 usage for a private key decryption. That way the device will prevent user access to the key once it is used to (partially) decrypt the data. As long as the encryption algorithm stays secure, it will become practically impossible to decrypt any data protected by that particular key.
Of course, the entity that just read the data now has the responsibility of keeping the information confidential. I can read a book and then burn it, but now the information in the book is (partially and inefficiently) stored in my memory after all. Reading data does mean that the data is duplicated in another location; reading fundamentally doesn't seem to be destruction of information, rather the propagation of information.
In short, no, I don't think we have a way to do this, but cryptography can certainly help by limiting the requirements for destruction to just a key rather than, for instance, a disk full of information.