Easiest way to proceed, to my mind is to do the following (fair warning though, this is dirty):

Split the multifasta up first:

#!/bin/bash
i=1;
while read line ; do
  if [ ${line:0:1} == ">" ] ; then
    header="$line"
    echo "$header" >> seq"${i}".fasta
  else
    seq="$line"
    echo "$seq" >> seq"${i}".fasta
    ((i++))
  fi
done < myalignment.fasta

Assuming your human reference sequence is always the first one, this script will generate a file for each, e.g. seq1.fasta, seq2.fasta, seq3.fasta etc.

This means your reference should always be the first seq1.fasta.

Then to remove the gaps, you can simply do sed -i 's/-//g' seq1.fasta.

Then concatenate them all back together if you need a multifasta again:

cat seq*.fasta > edited_multifasta.fasta