
I often wash my sofa seat covers & tumble dry them (on high heat). They do appear to be a little smaller once dried, but they seem to be smaller if line dried too, I think it's due to them shrinking back to the origional size .
Being sat on must stretch them out a bit - the same as clothes, if you put a tight pair of jeans on, in a couple of hours they have loosened up & washing them will take that stretch back out.
My last sofa used to get the covers washed & tumble dried often ( the kids were young- it was
cream 
) - it had a dry-clean only warning on it, they were always fine.
Just make sure that when washing/drying them the zips are done up and undo/do-up the zips carefully when putting covers back on , as you tend to get loose threads that catch in the zips
(washed my covers loads thanks to the dog peeing on them!).
ETA, hubby used to work as an upholsterer, the covers are meant to be a tight fit, there is a knack to getting them back in again.