Abstract In quantum theory, a quantum state on a composite system 
of two parties
realizes a non-negative probability with 
any measurement element with a tensor product form.
However, there also exist non-quantum states which satisfy the above condition.
Such states are called beyond-quantum states, and cannot be detected by standard Bell tests. 
To distinguish a beyond-quantum state from quantum states,
we propose a measurement-device-independent (MDI) test for beyond-quantum state detection, which is composed of 
quantum input states on respective parties and
quantum measurements across the input system and the target system on respective parties. 
The performance of our protocol is independent of 
the forms of the tested states and the measurement operators, which provides an advantage in practical scenarios.
We also discuss the importance of
tomographic completeness of the input sets to the detection.