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As suggested by rburing, I installed the (Ubuntu packages) openmpi-bin and openmpi-common via the system package manager and mpi4py with sage -pip install mpi4py. The application can be run according to the mpi4py tutorial. On Ubuntu 18.04, an additional problem was an out of date version of libstdc++. It can be upgraded as explained in this StackOverflow discussion.

$ sudo apt-get install openmpi-bin openmpi-common 
$ sage -pip install mpi4py
$ mpiexec -n 1 sage main_mpi.sage