How in hell...

Muting in the middle of a chords is quite hard

and the Fma7 is not the standard fingering ( so check your notation and try alternatives)

there are various techniques but it will depend on the chord and the style of the piece

you might try a partial barre with the first finger firmly on the 6th string and resting lightly on the fifth

heres another that shows possibilities scroll to the bottom you may have to register but i dont think it will cost anything   http://www.guitartricks.com/lesson.php?input=9738

Hi lextalionis
It's all a question of making your guitar playing easier for yourself and not to get hung up to much on fundamentals.
Sure some chords seem to require almost impossible string damping to bring off as by the book.
But as you say if they are in the middle of a song which probally has singing going on over the top a undampened string in the chord is not going to be heard and won't really change much in the sound of the song.
As Roger says theres nearly always a workable variation of the chord you want to play with an  easier shape.
Ark

That is the way to mute the 5th string and  play that chord.   it is a little easier to move it to the 3rd or 5th fret to practice
I know this is an old thread, but I thought I might provide a little additional information about the maj7 chord from the original question.   

That fingering is actually a pretty common jazz voicing.  I use it a lot with the G6 at the 3rd fret.
G6 3x243x
Gmaj7 3x443x

Gmaj7 G6 
VV      VV

And the form is easily movable up and down the fretboard where the 6th string is the root.  Good practice riff to learn to mute strings, but not so easy.

btw: xx3210 is an open alternative at the 1st fret someone else may have already mentioned.