No, not a Grundtvig original - he based his hymn on one by Biørn Christian Lund: 'Naar jeg Gethsemane her faar'

Oh Jesu mine, may my heart learn

Oh Jesu mine, may my heart learn

for you to hunger so

that night and day my soul will yearn

you never to forgo!

Then mercy’s time and hour shall be

most sweet and joyous too,

until one day your kiss takes me

from this life home to you.

In that same grave where you did bide

till Easter morn’s first breath,

may my heart rest at eventide

and smile at its own death!

Then take me home, poor sinner I,

in righteousness and love

to your Jerusalem on high,

to glory up above!

For more information, plus a quotation from Lund's original, go to here