  The low-mass star GJ 1151 has been reported to display variable low-frequency
radio emission, which has been interpreted as a signpost of coronal star-planet
interactions with an unseen exoplanet. Here we report the first X-ray detection
of GJ 1151's corona based on XMM-Newton data. We find that the star displays a
small flare during the X-ray observation. Averaged over the observation, we
detect the star with a low coronal temperature of 1.6~MK and an X-ray
luminosity of $L_X = 5.5\times 10^{26}$\,erg/s. During the quiescent time
periods excluding the flare, the star remains undetected with an upper limit of
$L_{X,\,qui} \leq 3.7\times 10^{26}$\,erg/s. This is compatible with the
coronal assumptions used in a recently published model for a star-planet
interaction origin of the observed radio signals from this star.
