Use NamedTemporaryFile to create the input file. If you close it, there should be no drain on file descriptors.
f=tempfile.NamedTemporaryFile(delete=True)
region=tempfile.NamedTemporaryFile(delete=False)
region.write(b'chr1\t1090917\t1136917\n')
region.close()
subprocess.call(['/usr/local/bin/shuffleBed', '-incl',region.name,'-i','temp'+chromosome+'ShuffleMutations.bed','-g','hg19.genome'],stdout=f)