I see this in Call Ducks very often. Most of the time it is a blood circulation problem. Ive seen them come out of it, and Ive seen the die from it, and sometimes they just live with it! It could of broke its leg or strained some tendents in its leg.
Sadly my little duckling got this at a few weeks old, I found out it was rickets.. I tried splinting the legs to no avail... it was not growing properly either, I tried brewers yeast in food ect but nothing would work, so sadly it was put to sleep
I had this happen to a runner once it was during cold weather and pretty muddy outside (snow melting) so I held her and put her in warm water to clean her off, then wrapped her up in a towel under a heat lamp and the next morning she was fine...so maybe there's hope for yours