while listening to the part (great song by the way), i am hearing just a very slight growl and not to much distortion. As the the previous comments mentioned, this is very likely the combination of EQ and compression.
As I believe Donald "Duck" Dunn did the bass part for this song, I would start with researching how he builds up his sound and what he uses.
Of course it is all in the fingers and we can never be the late great Duck Dunn, however you could start with his amp+cab which I believe is Ampeg and experiment by adding compression and eq.
Find some other songs and articles which are widely available (youtube etc) to find out more about his sound and technique
I really like this bass sound, might actually try to re-create one and post it :-)
...hope this helps....