It depends on the conditions of the question and what assumptions you are expected to make.
For a system as a whole, momentum is always conserved if there are no external forces, even though kinetic energy has increased. (Chemical energy has been converted into kinetic energy.) However, if the mass of "the system" changes then total momentum might change also.
If the spacecraft breaks up into only two parts, the total momentum of those two parts will be conserved in the explosion. The total mass of the system is the same. This assumes either that the mass of the fuel can be neglected compared with that of the two parts of the spacecraft, or that the fuel somehow remains stuck to one or both of the two parts.
However, if the fuel is expelled as in a rocket and it has significant mass, then effectively the spacecraft has broken into 3 or more parts. The total momentum of the 3 or more parts is conserved. But if you ignore the ejected fuel and consider only the momenta of the 2 main parts then momentum is not necessarily conserved. In this case the mass of the system has changed.