Ah, figured it out:
3dCalc \
-a 'filename+orig' \
-dsWRAP \
-b 'a[0,-6,0,0]' \
-expr '(b)' \
-prefix savefilename
where [i,j,k,t] means translation in any of the directions and '-dsWRAP' is to wrap around. More info can be found in the manual for 3dCalc.