Are they just as close as English and German? Has Swedish also suffered some phonological influences from German during the Hansatic league?
“Closeness” and “mutual intelligibility” are two separate issues. German is widely taught in schools in the Scandinavian countries, so most people there can understand German to some extent. A further issue is that Swedish, Norwegian and Danish have lots of loanwords from High and Low German, as well as many international (Latin, Greek, French, English) words shared also by German. None of this has anything to do with genetic closeness.