Context : Brown dwarf companions to stars at separations of a few AU or less are rare objects , and none have been found so far around early-type M dwarfs ( M0V-M5V ) . With GJ 1046 ( M2.5V ) , a strong candidate for such a system with a separation of 0.42 ~ { } \mathrm { AU } is presented . Aims : We aim at constraining the mass of the companion in order to decide whether it is a brown dwarf or a low-mass star . Methods : We employed precision RV measurements to determine the orbital parameters and the minimum companion mass . We then derived an upper limit to the companion mass from the lack of disturbances of the RV measurements by a secondary spectrum . An even tighter upper limit is subsequently established by combining the RV-derived orbital parameters with the recent new version of the Hipparcos Intermediate Astrometric Data . Results : For the mass of the companion , we derive m \geq 26.9 ~ { } \mathrm { M } _ { \mathrm { Jup } } from the RV data . Based on the RV data alone , the probability that the companion exceeds the stellar mass threshold is just 6.2 \% . The absence of effects from the secondary spectrum lets us constrain the companion mass to m \leq 229 ~ { } \mathrm { M } _ { \mathrm { Jup } } . The combination of RV and Hipparcos data yields a 3 \sigma upper mass limit to the companion mass of 112 ~ { } \mathrm { M } _ { \mathrm { Jup } } with a formal optimum value at m = 47.2 ~ { } \mathrm { M } _ { \mathrm { Jup } } . From the combination of RV and astrometric data , the chance probability that the companion is a star is 2.9 \% . Conclusions : We have found a low-mass , close companion to an early-type M dwarf . While the most likely interpretation of this object is that it is a brown dwarf , a low-mass stellar companion is not fully excluded .