The answer to this question can be found in Act II, which is when Gregers visits Hjalmar's appartment and is shown by Hjalmar's father the various animals that they keep, including the wild duck, that was given to Hedvig. Ekdal explains how, indirectly, the duck was given to Hedvig by the father of Gregers, as he shot a duck, but missed killing it outright. The duck then dove to the bottom of the lake, but Hakon's dog retrieved it. Pettersen, Hakon's manservant, was told to kill the duck, but Ekdal persuaded him to give it to him and he gave the wild duck to Hedvig. Of course the play's title identifies what a massively important symbol this wild duck is. Note how Ekdal explains why Hakon only wounded the duck:
He was shooting from a boat, you see, and he brought her down. But your father's sight is not very good now. H'm; she was only wounded.
This is of course an important clue that links Hedvig's encroaching blindness to the identity of her father, who, the play strongly suggests, is the product of Hakon's illegitimate affair with Gina before she married Hjalmar. But also, the wild duck stands as a symbol of the impact that Hakon has on Gina and her new family, keeping them in their "wounded" state through his generosity just as the wild duck is kept by Hedvig, being unable to fly.